Distancia Entre Matrices de Covarianza
Edgar Espejo
2022-12-13
Comparación de fotos de los tipos de fracturas
# libreria de lectura de bitmaps para bmp, jpeg, png y tiff
library(readbitmap)## Warning: package 'readbitmap' was built under R version 4.1.2library(fda)## Warning: package 'fda' was built under R version 4.1.3## Loading required package: splines## Loading required package: fds## Warning: package 'fds' was built under R version 4.1.3## Loading required package: rainbow## Warning: package 'rainbow' was built under R version 4.1.3## Loading required package: MASS## Warning: package 'MASS' was built under R version 4.1.3## Loading required package: pcaPP## Warning: package 'pcaPP' was built under R version 4.1.3## Loading required package: RCurl## Warning: package 'RCurl' was built under R version 4.1.3## Loading required package: deSolve## Warning: package 'deSolve' was built under R version 4.1.3##
## Attaching package: 'fda'## The following object is masked from 'package:graphics':
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## matplotlibrary(ggplot2)## Warning: package 'ggplot2' was built under R version 4.1.3library(dplyr)## Warning: package 'dplyr' was built under R version 4.1.3##
## Attaching package: 'dplyr'## The following object is masked from 'package:MASS':
##
## select## The following objects are masked from 'package:stats':
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## filter, lag## The following objects are masked from 'package:base':
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## intersect, setdiff, setequal, unionlibrary(caret)## Warning: package 'caret' was built under R version 4.1.3## Loading required package: lattice## Warning: package 'lattice' was built under R version 4.1.3##
## Attaching package: 'lattice'## The following object is masked from 'package:fda':
##
## melanomalibrary(shapes)## Warning: package 'shapes' was built under R version 4.1.31. Cargar imagenes dúctiles
Total de imagenes 10. Por cada foto 400 datos funcionales (lineas de pixeles en X y líneas de pixeles en y), para un total de 4000 datos.
imagenductilent1 <- read.bitmap("DuctilEnt1.jpg") # crea una matriz de x filas y columanas y z=3 canales
imagenductilent1 <- imagenductilent1 [,,1] # Deja un solo canal
imagenductilent1t <- t(imagenductilent1)
imagenductilent1xey <- rbind(imagenductilent1,imagenductilent1t)
imagenductilent1xey <- t(imagenductilent1xey)
dim(imagenductilent1xey)## [1] 200 400imagenductilent2 <- read.bitmap("DuctilEnt2.jpg") # crea una matriz de x filas y columanas y z=3 canales
imagenductilent2 <- imagenductilent2 [,,1] # Deja un solo canal
imagenductilent2t <- t(imagenductilent2)
imagenductilent2xey <- rbind(imagenductilent2,imagenductilent2t)
imagenductilent2xey <- t(imagenductilent2xey)
dim(imagenductilent2xey)## [1] 200 400imagenductilent3 <- read.bitmap("DuctilEnt3.jpg") # crea una matriz de x filas y columanas y z=3 canales
imagenductilent3 <- imagenductilent3 [,,1] # Deja un solo canal
imagenductilent3t <- t(imagenductilent3)
imagenductilent3xey <- rbind(imagenductilent3,imagenductilent3t)
imagenductilent3xey <- t(imagenductilent3xey)
dim(imagenductilent3xey)## [1] 200 400imagenductilent4 <- read.bitmap("DuctilEnt4.jpg") # crea una matriz de x filas y columanas y z=3 canales
imagenductilent4 <- imagenductilent4 [,,1] # Deja un solo canal
imagenductilent4t <- t(imagenductilent4)
imagenductilent4xey <- rbind(imagenductilent4,imagenductilent4t)
imagenductilent4xey <- t(imagenductilent4xey)
dim(imagenductilent4xey)## [1] 200 400imagenductilent5 <- read.bitmap("DuctilEnt5.jpg") # crea una matriz de x filas y columanas y z=3 canales
imagenductilent5 <- imagenductilent5 [,,1] # Deja un solo canal
imagenductilent5t <- t(imagenductilent5)
imagenductilent5xey <- rbind(imagenductilent5,imagenductilent5t)
imagenductilent5xey <- t(imagenductilent5xey)
dim(imagenductilent5xey)## [1] 200 400imagenductilent6 <- read.bitmap("DuctilEnt6.jpg") # crea una matriz de x filas y columanas y z=3 canales
imagenductilent6 <- imagenductilent6 [,,1] # Deja un solo canal
imagenductilent6t <- t(imagenductilent6)
imagenductilent6xey <- rbind(imagenductilent6,imagenductilent6t)
imagenductilent6xey <- t(imagenductilent6xey)
dim(imagenductilent6xey)## [1] 200 400imagenductilent7 <- read.bitmap("DuctilEnt7.jpg") # crea una matriz de x filas y columanas y z=3 canales
imagenductilent7 <- imagenductilent7 [,,1] # Deja un solo canal
imagenductilent7t <- t(imagenductilent7)
imagenductilent7xey <- rbind(imagenductilent7,imagenductilent7t)
imagenductilent7xey <- t(imagenductilent7xey)
dim(imagenductilent7xey)## [1] 200 400imagenductilens1 <- read.bitmap("DuctilEns1.jpg") # crea una matriz de x filas y columanas y z=3 canales
imagenductilens1 <- imagenductilens1 [,,1] # Deja un solo canal
imagenductilens1t <- t(imagenductilens1)
imagenductilens1xey <- rbind(imagenductilens1,imagenductilens1t)
imagenductilens1xey <- t(imagenductilens1xey)
dim(imagenductilens1xey)## [1] 200 400imagenductilens2 <- read.bitmap("DuctilEns2.jpg") # crea una matriz de x filas y columanas y z=3 canales
imagenductilens2 <- imagenductilens2 [,,1] # Deja un solo canal
imagenductilens2t <- t(imagenductilens2)
imagenductilens2xey <- rbind(imagenductilens2,imagenductilens2t)
imagenductilens2xey <- t(imagenductilens2xey)
dim(imagenductilens2xey)## [1] 200 400imagenductilens3 <- read.bitmap("DuctilEns3.jpg") # crea una matriz de x filas y columanas y z=3 canales
imagenductilens3 <- imagenductilens3 [,,1] # Deja un solo canal
imagenductilens3t <- t(imagenductilens3)
imagenductilens3xey <- rbind(imagenductilens3,imagenductilens3t)
imagenductilens3xey <- t(imagenductilens3xey)
dim(imagenductilens3xey)## [1] 200 400imagenductilxey <- cbind(imagenductilent1xey,imagenductilent2xey,imagenductilent3xey,imagenductilent4xey,imagenductilent5xey,imagenductilent6xey,imagenductilent7xey,imagenductilens1xey,imagenductilens2xey,imagenductilens3xey)
dim(imagenductilxey)## [1] 200 4000# Convertir en Data Frame Ductil
imagenductilxeydf <- as.data.frame (imagenductilxey)
attributes(imagenductilxeydf)## $names
## [1] "V1" "V2" "V3" "V4" "V5" "V6" "V7" "V8" "V9"
## [10] "V10" "V11" "V12" "V13" "V14" "V15" "V16" "V17" "V18"
## [19] "V19" "V20" "V21" "V22" "V23" "V24" "V25" "V26" "V27"
## [28] "V28" "V29" "V30" "V31" "V32" "V33" "V34" "V35" "V36"
## [37] "V37" "V38" "V39" "V40" "V41" "V42" "V43" "V44" "V45"
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## [361] "V361" "V362" "V363" "V364" "V365" "V366" "V367" "V368" "V369"
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## [379] "V379" "V380" "V381" "V382" "V383" "V384" "V385" "V386" "V387"
## [388] "V388" "V389" "V390" "V391" "V392" "V393" "V394" "V395" "V396"
## [397] "V397" "V398" "V399" "V400" "V401" "V402" "V403" "V404" "V405"
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## [415] "V415" "V416" "V417" "V418" "V419" "V420" "V421" "V422" "V423"
## [424] "V424" "V425" "V426" "V427" "V428" "V429" "V430" "V431" "V432"
## [433] "V433" "V434" "V435" "V436" "V437" "V438" "V439" "V440" "V441"
## [442] "V442" "V443" "V444" "V445" "V446" "V447" "V448" "V449" "V450"
## [451] "V451" "V452" "V453" "V454" "V455" "V456" "V457" "V458" "V459"
## [460] "V460" "V461" "V462" "V463" "V464" "V465" "V466" "V467" "V468"
## [469] "V469" "V470" "V471" "V472" "V473" "V474" "V475" "V476" "V477"
## [478] "V478" "V479" "V480" "V481" "V482" "V483" "V484" "V485" "V486"
## [487] "V487" "V488" "V489" "V490" "V491" "V492" "V493" "V494" "V495"
## [496] "V496" "V497" "V498" "V499" "V500" "V501" "V502" "V503" "V504"
## [505] "V505" "V506" "V507" "V508" "V509" "V510" "V511" "V512" "V513"
## [514] "V514" "V515" "V516" "V517" "V518" "V519" "V520" "V521" "V522"
## [523] "V523" "V524" "V525" "V526" "V527" "V528" "V529" "V530" "V531"
## [532] "V532" "V533" "V534" "V535" "V536" "V537" "V538" "V539" "V540"
## [541] "V541" "V542" "V543" "V544" "V545" "V546" "V547" "V548" "V549"
## [550] "V550" "V551" "V552" "V553" "V554" "V555" "V556" "V557" "V558"
## [559] "V559" "V560" "V561" "V562" "V563" "V564" "V565" "V566" "V567"
## [568] "V568" "V569" "V570" "V571" "V572" "V573" "V574" "V575" "V576"
## [577] "V577" "V578" "V579" "V580" "V581" "V582" "V583" "V584" "V585"
## [586] "V586" "V587" "V588" "V589" "V590" "V591" "V592" "V593" "V594"
## [595] "V595" "V596" "V597" "V598" "V599" "V600" "V601" "V602" "V603"
## [604] "V604" "V605" "V606" "V607" "V608" "V609" "V610" "V611" "V612"
## [613] "V613" "V614" "V615" "V616" "V617" "V618" "V619" "V620" "V621"
## [622] "V622" "V623" "V624" "V625" "V626" "V627" "V628" "V629" "V630"
## [631] "V631" "V632" "V633" "V634" "V635" "V636" "V637" "V638" "V639"
## [640] "V640" "V641" "V642" "V643" "V644" "V645" "V646" "V647" "V648"
## [649] "V649" "V650" "V651" "V652" "V653" "V654" "V655" "V656" "V657"
## [658] "V658" "V659" "V660" "V661" "V662" "V663" "V664" "V665" "V666"
## [667] "V667" "V668" "V669" "V670" "V671" "V672" "V673" "V674" "V675"
## [676] "V676" "V677" "V678" "V679" "V680" "V681" "V682" "V683" "V684"
## [685] "V685" "V686" "V687" "V688" "V689" "V690" "V691" "V692" "V693"
## [694] "V694" "V695" "V696" "V697" "V698" "V699" "V700" "V701" "V702"
## [703] "V703" "V704" "V705" "V706" "V707" "V708" "V709" "V710" "V711"
## [712] "V712" "V713" "V714" "V715" "V716" "V717" "V718" "V719" "V720"
## [721] "V721" "V722" "V723" "V724" "V725" "V726" "V727" "V728" "V729"
## [730] "V730" "V731" "V732" "V733" "V734" "V735" "V736" "V737" "V738"
## [739] "V739" "V740" "V741" "V742" "V743" "V744" "V745" "V746" "V747"
## [748] "V748" "V749" "V750" "V751" "V752" "V753" "V754" "V755" "V756"
## [757] "V757" "V758" "V759" "V760" "V761" "V762" "V763" "V764" "V765"
## [766] "V766" "V767" "V768" "V769" "V770" "V771" "V772" "V773" "V774"
## [775] "V775" "V776" "V777" "V778" "V779" "V780" "V781" "V782" "V783"
## [784] "V784" "V785" "V786" "V787" "V788" "V789" "V790" "V791" "V792"
## [793] "V793" "V794" "V795" "V796" "V797" "V798" "V799" "V800" "V801"
## [802] "V802" "V803" "V804" "V805" "V806" "V807" "V808" "V809" "V810"
## [811] "V811" "V812" "V813" "V814" "V815" "V816" "V817" "V818" "V819"
## [820] "V820" "V821" "V822" "V823" "V824" "V825" "V826" "V827" "V828"
## [829] "V829" "V830" "V831" "V832" "V833" "V834" "V835" "V836" "V837"
## [838] "V838" "V839" "V840" "V841" "V842" "V843" "V844" "V845" "V846"
## [847] "V847" "V848" "V849" "V850" "V851" "V852" "V853" "V854" "V855"
## [856] "V856" "V857" "V858" "V859" "V860" "V861" "V862" "V863" "V864"
## [865] "V865" "V866" "V867" "V868" "V869" "V870" "V871" "V872" "V873"
## [874] "V874" "V875" "V876" "V877" "V878" "V879" "V880" "V881" "V882"
## [883] "V883" "V884" "V885" "V886" "V887" "V888" "V889" "V890" "V891"
## [892] "V892" "V893" "V894" "V895" "V896" "V897" "V898" "V899" "V900"
## [901] "V901" "V902" "V903" "V904" "V905" "V906" "V907" "V908" "V909"
## [910] "V910" "V911" "V912" "V913" "V914" "V915" "V916" "V917" "V918"
## [919] "V919" "V920" "V921" "V922" "V923" "V924" "V925" "V926" "V927"
## [928] "V928" "V929" "V930" "V931" "V932" "V933" "V934" "V935" "V936"
## [937] "V937" "V938" "V939" "V940" "V941" "V942" "V943" "V944" "V945"
## [946] "V946" "V947" "V948" "V949" "V950" "V951" "V952" "V953" "V954"
## [955] "V955" "V956" "V957" "V958" "V959" "V960" "V961" "V962" "V963"
## [964] "V964" "V965" "V966" "V967" "V968" "V969" "V970" "V971" "V972"
## [973] "V973" "V974" "V975" "V976" "V977" "V978" "V979" "V980" "V981"
## [982] "V982" "V983" "V984" "V985" "V986" "V987" "V988" "V989" "V990"
## [991] "V991" "V992" "V993" "V994" "V995" "V996" "V997" "V998" "V999"
## [1000] "V1000" "V1001" "V1002" "V1003" "V1004" "V1005" "V1006" "V1007" "V1008"
## [1009] "V1009" "V1010" "V1011" "V1012" "V1013" "V1014" "V1015" "V1016" "V1017"
## [1018] "V1018" "V1019" "V1020" "V1021" "V1022" "V1023" "V1024" "V1025" "V1026"
## [1027] "V1027" "V1028" "V1029" "V1030" "V1031" "V1032" "V1033" "V1034" "V1035"
## [1036] "V1036" "V1037" "V1038" "V1039" "V1040" "V1041" "V1042" "V1043" "V1044"
## [1045] "V1045" "V1046" "V1047" "V1048" "V1049" "V1050" "V1051" "V1052" "V1053"
## [1054] "V1054" "V1055" "V1056" "V1057" "V1058" "V1059" "V1060" "V1061" "V1062"
## [1063] "V1063" "V1064" "V1065" "V1066" "V1067" "V1068" "V1069" "V1070" "V1071"
## [1072] "V1072" "V1073" "V1074" "V1075" "V1076" "V1077" "V1078" "V1079" "V1080"
## [1081] "V1081" "V1082" "V1083" "V1084" "V1085" "V1086" "V1087" "V1088" "V1089"
## [1090] "V1090" "V1091" "V1092" "V1093" "V1094" "V1095" "V1096" "V1097" "V1098"
## [1099] "V1099" "V1100" "V1101" "V1102" "V1103" "V1104" "V1105" "V1106" "V1107"
## [1108] "V1108" "V1109" "V1110" "V1111" "V1112" "V1113" "V1114" "V1115" "V1116"
## [1117] "V1117" "V1118" "V1119" "V1120" "V1121" "V1122" "V1123" "V1124" "V1125"
## [1126] "V1126" "V1127" "V1128" "V1129" "V1130" "V1131" "V1132" "V1133" "V1134"
## [1135] "V1135" "V1136" "V1137" "V1138" "V1139" "V1140" "V1141" "V1142" "V1143"
## [1144] "V1144" "V1145" "V1146" "V1147" "V1148" "V1149" "V1150" "V1151" "V1152"
## [1153] "V1153" "V1154" "V1155" "V1156" "V1157" "V1158" "V1159" "V1160" "V1161"
## [1162] "V1162" "V1163" "V1164" "V1165" "V1166" "V1167" "V1168" "V1169" "V1170"
## [1171] "V1171" "V1172" "V1173" "V1174" "V1175" "V1176" "V1177" "V1178" "V1179"
## [1180] "V1180" "V1181" "V1182" "V1183" "V1184" "V1185" "V1186" "V1187" "V1188"
## [1189] "V1189" "V1190" "V1191" "V1192" "V1193" "V1194" "V1195" "V1196" "V1197"
## [1198] "V1198" "V1199" "V1200" "V1201" "V1202" "V1203" "V1204" "V1205" "V1206"
## [1207] "V1207" "V1208" "V1209" "V1210" "V1211" "V1212" "V1213" "V1214" "V1215"
## [1216] "V1216" "V1217" "V1218" "V1219" "V1220" "V1221" "V1222" "V1223" "V1224"
## [1225] "V1225" "V1226" "V1227" "V1228" "V1229" "V1230" "V1231" "V1232" "V1233"
## [1234] "V1234" "V1235" "V1236" "V1237" "V1238" "V1239" "V1240" "V1241" "V1242"
## [1243] "V1243" "V1244" "V1245" "V1246" "V1247" "V1248" "V1249" "V1250" "V1251"
## [1252] "V1252" "V1253" "V1254" "V1255" "V1256" "V1257" "V1258" "V1259" "V1260"
## [1261] "V1261" "V1262" "V1263" "V1264" "V1265" "V1266" "V1267" "V1268" "V1269"
## [1270] "V1270" "V1271" "V1272" "V1273" "V1274" "V1275" "V1276" "V1277" "V1278"
## [1279] "V1279" "V1280" "V1281" "V1282" "V1283" "V1284" "V1285" "V1286" "V1287"
## [1288] "V1288" "V1289" "V1290" "V1291" "V1292" "V1293" "V1294" "V1295" "V1296"
## [1297] "V1297" "V1298" "V1299" "V1300" "V1301" "V1302" "V1303" "V1304" "V1305"
## [1306] "V1306" "V1307" "V1308" "V1309" "V1310" "V1311" "V1312" "V1313" "V1314"
## [1315] "V1315" "V1316" "V1317" "V1318" "V1319" "V1320" "V1321" "V1322" "V1323"
## [1324] "V1324" "V1325" "V1326" "V1327" "V1328" "V1329" "V1330" "V1331" "V1332"
## [1333] "V1333" "V1334" "V1335" "V1336" "V1337" "V1338" "V1339" "V1340" "V1341"
## [1342] "V1342" "V1343" "V1344" "V1345" "V1346" "V1347" "V1348" "V1349" "V1350"
## [1351] "V1351" "V1352" "V1353" "V1354" "V1355" "V1356" "V1357" "V1358" "V1359"
## [1360] "V1360" "V1361" "V1362" "V1363" "V1364" "V1365" "V1366" "V1367" "V1368"
## [1369] "V1369" "V1370" "V1371" "V1372" "V1373" "V1374" "V1375" "V1376" "V1377"
## [1378] "V1378" "V1379" "V1380" "V1381" "V1382" "V1383" "V1384" "V1385" "V1386"
## [1387] "V1387" "V1388" "V1389" "V1390" "V1391" "V1392" "V1393" "V1394" "V1395"
## [1396] "V1396" "V1397" "V1398" "V1399" "V1400" "V1401" "V1402" "V1403" "V1404"
## [1405] "V1405" "V1406" "V1407" "V1408" "V1409" "V1410" "V1411" "V1412" "V1413"
## [1414] "V1414" "V1415" "V1416" "V1417" "V1418" "V1419" "V1420" "V1421" "V1422"
## [1423] "V1423" "V1424" "V1425" "V1426" "V1427" "V1428" "V1429" "V1430" "V1431"
## [1432] "V1432" "V1433" "V1434" "V1435" "V1436" "V1437" "V1438" "V1439" "V1440"
## [1441] "V1441" "V1442" "V1443" "V1444" "V1445" "V1446" "V1447" "V1448" "V1449"
## [1450] "V1450" "V1451" "V1452" "V1453" "V1454" "V1455" "V1456" "V1457" "V1458"
## [1459] "V1459" "V1460" "V1461" "V1462" "V1463" "V1464" "V1465" "V1466" "V1467"
## [1468] "V1468" "V1469" "V1470" "V1471" "V1472" "V1473" "V1474" "V1475" "V1476"
## [1477] "V1477" "V1478" "V1479" "V1480" "V1481" "V1482" "V1483" "V1484" "V1485"
## [1486] "V1486" "V1487" "V1488" "V1489" "V1490" "V1491" "V1492" "V1493" "V1494"
## [1495] "V1495" "V1496" "V1497" "V1498" "V1499" "V1500" "V1501" "V1502" "V1503"
## [1504] "V1504" "V1505" "V1506" "V1507" "V1508" "V1509" "V1510" "V1511" "V1512"
## [1513] "V1513" "V1514" "V1515" "V1516" "V1517" "V1518" "V1519" "V1520" "V1521"
## [1522] "V1522" "V1523" "V1524" "V1525" "V1526" "V1527" "V1528" "V1529" "V1530"
## [1531] "V1531" "V1532" "V1533" "V1534" "V1535" "V1536" "V1537" "V1538" "V1539"
## [1540] "V1540" "V1541" "V1542" "V1543" "V1544" "V1545" "V1546" "V1547" "V1548"
## [1549] "V1549" "V1550" "V1551" "V1552" "V1553" "V1554" "V1555" "V1556" "V1557"
## [1558] "V1558" "V1559" "V1560" "V1561" "V1562" "V1563" "V1564" "V1565" "V1566"
## [1567] "V1567" "V1568" "V1569" "V1570" "V1571" "V1572" "V1573" "V1574" "V1575"
## [1576] "V1576" "V1577" "V1578" "V1579" "V1580" "V1581" "V1582" "V1583" "V1584"
## [1585] "V1585" "V1586" "V1587" "V1588" "V1589" "V1590" "V1591" "V1592" "V1593"
## [1594] "V1594" "V1595" "V1596" "V1597" "V1598" "V1599" "V1600" "V1601" "V1602"
## [1603] "V1603" "V1604" "V1605" "V1606" "V1607" "V1608" "V1609" "V1610" "V1611"
## [1612] "V1612" "V1613" "V1614" "V1615" "V1616" "V1617" "V1618" "V1619" "V1620"
## [1621] "V1621" "V1622" "V1623" "V1624" "V1625" "V1626" "V1627" "V1628" "V1629"
## [1630] "V1630" "V1631" "V1632" "V1633" "V1634" "V1635" "V1636" "V1637" "V1638"
## [1639] "V1639" "V1640" "V1641" "V1642" "V1643" "V1644" "V1645" "V1646" "V1647"
## [1648] "V1648" "V1649" "V1650" "V1651" "V1652" "V1653" "V1654" "V1655" "V1656"
## [1657] "V1657" "V1658" "V1659" "V1660" "V1661" "V1662" "V1663" "V1664" "V1665"
## [1666] "V1666" "V1667" "V1668" "V1669" "V1670" "V1671" "V1672" "V1673" "V1674"
## [1675] "V1675" "V1676" "V1677" "V1678" "V1679" "V1680" "V1681" "V1682" "V1683"
## [1684] "V1684" "V1685" "V1686" "V1687" "V1688" "V1689" "V1690" "V1691" "V1692"
## [1693] "V1693" "V1694" "V1695" "V1696" "V1697" "V1698" "V1699" "V1700" "V1701"
## [1702] "V1702" "V1703" "V1704" "V1705" "V1706" "V1707" "V1708" "V1709" "V1710"
## [1711] "V1711" "V1712" "V1713" "V1714" "V1715" "V1716" "V1717" "V1718" "V1719"
## [1720] "V1720" "V1721" "V1722" "V1723" "V1724" "V1725" "V1726" "V1727" "V1728"
## [1729] "V1729" "V1730" "V1731" "V1732" "V1733" "V1734" "V1735" "V1736" "V1737"
## [1738] "V1738" "V1739" "V1740" "V1741" "V1742" "V1743" "V1744" "V1745" "V1746"
## [1747] "V1747" "V1748" "V1749" "V1750" "V1751" "V1752" "V1753" "V1754" "V1755"
## [1756] "V1756" "V1757" "V1758" "V1759" "V1760" "V1761" "V1762" "V1763" "V1764"
## [1765] "V1765" "V1766" "V1767" "V1768" "V1769" "V1770" "V1771" "V1772" "V1773"
## [1774] "V1774" "V1775" "V1776" "V1777" "V1778" "V1779" "V1780" "V1781" "V1782"
## [1783] "V1783" "V1784" "V1785" "V1786" "V1787" "V1788" "V1789" "V1790" "V1791"
## [1792] "V1792" "V1793" "V1794" "V1795" "V1796" "V1797" "V1798" "V1799" "V1800"
## [1801] "V1801" "V1802" "V1803" "V1804" "V1805" "V1806" "V1807" "V1808" "V1809"
## [1810] "V1810" "V1811" "V1812" "V1813" "V1814" "V1815" "V1816" "V1817" "V1818"
## [1819] "V1819" "V1820" "V1821" "V1822" "V1823" "V1824" "V1825" "V1826" "V1827"
## [1828] "V1828" "V1829" "V1830" "V1831" "V1832" "V1833" "V1834" "V1835" "V1836"
## [1837] "V1837" "V1838" "V1839" "V1840" "V1841" "V1842" "V1843" "V1844" "V1845"
## [1846] "V1846" "V1847" "V1848" "V1849" "V1850" "V1851" "V1852" "V1853" "V1854"
## [1855] "V1855" "V1856" "V1857" "V1858" "V1859" "V1860" "V1861" "V1862" "V1863"
## [1864] "V1864" "V1865" "V1866" "V1867" "V1868" "V1869" "V1870" "V1871" "V1872"
## [1873] "V1873" "V1874" "V1875" "V1876" "V1877" "V1878" "V1879" "V1880" "V1881"
## [1882] "V1882" "V1883" "V1884" "V1885" "V1886" "V1887" "V1888" "V1889" "V1890"
## [1891] "V1891" "V1892" "V1893" "V1894" "V1895" "V1896" "V1897" "V1898" "V1899"
## [1900] "V1900" "V1901" "V1902" "V1903" "V1904" "V1905" "V1906" "V1907" "V1908"
## [1909] "V1909" "V1910" "V1911" "V1912" "V1913" "V1914" "V1915" "V1916" "V1917"
## [1918] "V1918" "V1919" "V1920" "V1921" "V1922" "V1923" "V1924" "V1925" "V1926"
## [1927] "V1927" "V1928" "V1929" "V1930" "V1931" "V1932" "V1933" "V1934" "V1935"
## [1936] "V1936" "V1937" "V1938" "V1939" "V1940" "V1941" "V1942" "V1943" "V1944"
## [1945] "V1945" "V1946" "V1947" "V1948" "V1949" "V1950" "V1951" "V1952" "V1953"
## [1954] "V1954" "V1955" "V1956" "V1957" "V1958" "V1959" "V1960" "V1961" "V1962"
## [1963] "V1963" "V1964" "V1965" "V1966" "V1967" "V1968" "V1969" "V1970" "V1971"
## [1972] "V1972" "V1973" "V1974" "V1975" "V1976" "V1977" "V1978" "V1979" "V1980"
## [1981] "V1981" "V1982" "V1983" "V1984" "V1985" "V1986" "V1987" "V1988" "V1989"
## [1990] "V1990" "V1991" "V1992" "V1993" "V1994" "V1995" "V1996" "V1997" "V1998"
## [1999] "V1999" "V2000" "V2001" "V2002" "V2003" "V2004" "V2005" "V2006" "V2007"
## [2008] "V2008" "V2009" "V2010" "V2011" "V2012" "V2013" "V2014" "V2015" "V2016"
## [2017] "V2017" "V2018" "V2019" "V2020" "V2021" "V2022" "V2023" "V2024" "V2025"
## [2026] "V2026" "V2027" "V2028" "V2029" "V2030" "V2031" "V2032" "V2033" "V2034"
## [2035] "V2035" "V2036" "V2037" "V2038" "V2039" "V2040" "V2041" "V2042" "V2043"
## [2044] "V2044" "V2045" "V2046" "V2047" "V2048" "V2049" "V2050" "V2051" "V2052"
## [2053] "V2053" "V2054" "V2055" "V2056" "V2057" "V2058" "V2059" "V2060" "V2061"
## [2062] "V2062" "V2063" "V2064" "V2065" "V2066" "V2067" "V2068" "V2069" "V2070"
## [2071] "V2071" "V2072" "V2073" "V2074" "V2075" "V2076" "V2077" "V2078" "V2079"
## [2080] "V2080" "V2081" "V2082" "V2083" "V2084" "V2085" "V2086" "V2087" "V2088"
## [2089] "V2089" "V2090" "V2091" "V2092" "V2093" "V2094" "V2095" "V2096" "V2097"
## [2098] "V2098" "V2099" "V2100" "V2101" "V2102" "V2103" "V2104" "V2105" "V2106"
## [2107] "V2107" "V2108" "V2109" "V2110" "V2111" "V2112" "V2113" "V2114" "V2115"
## [2116] "V2116" "V2117" "V2118" "V2119" "V2120" "V2121" "V2122" "V2123" "V2124"
## [2125] "V2125" "V2126" "V2127" "V2128" "V2129" "V2130" "V2131" "V2132" "V2133"
## [2134] "V2134" "V2135" "V2136" "V2137" "V2138" "V2139" "V2140" "V2141" "V2142"
## [2143] "V2143" "V2144" "V2145" "V2146" "V2147" "V2148" "V2149" "V2150" "V2151"
## [2152] "V2152" "V2153" "V2154" "V2155" "V2156" "V2157" "V2158" "V2159" "V2160"
## [2161] "V2161" "V2162" "V2163" "V2164" "V2165" "V2166" "V2167" "V2168" "V2169"
## [2170] "V2170" "V2171" "V2172" "V2173" "V2174" "V2175" "V2176" "V2177" "V2178"
## [2179] "V2179" "V2180" "V2181" "V2182" "V2183" "V2184" "V2185" "V2186" "V2187"
## [2188] "V2188" "V2189" "V2190" "V2191" "V2192" "V2193" "V2194" "V2195" "V2196"
## [2197] "V2197" "V2198" "V2199" "V2200" "V2201" "V2202" "V2203" "V2204" "V2205"
## [2206] "V2206" "V2207" "V2208" "V2209" "V2210" "V2211" "V2212" "V2213" "V2214"
## [2215] "V2215" "V2216" "V2217" "V2218" "V2219" "V2220" "V2221" "V2222" "V2223"
## [2224] "V2224" "V2225" "V2226" "V2227" "V2228" "V2229" "V2230" "V2231" "V2232"
## [2233] "V2233" "V2234" "V2235" "V2236" "V2237" "V2238" "V2239" "V2240" "V2241"
## [2242] "V2242" "V2243" "V2244" "V2245" "V2246" "V2247" "V2248" "V2249" "V2250"
## [2251] "V2251" "V2252" "V2253" "V2254" "V2255" "V2256" "V2257" "V2258" "V2259"
## [2260] "V2260" "V2261" "V2262" "V2263" "V2264" "V2265" "V2266" "V2267" "V2268"
## [2269] "V2269" "V2270" "V2271" "V2272" "V2273" "V2274" "V2275" "V2276" "V2277"
## [2278] "V2278" "V2279" "V2280" "V2281" "V2282" "V2283" "V2284" "V2285" "V2286"
## [2287] "V2287" "V2288" "V2289" "V2290" "V2291" "V2292" "V2293" "V2294" "V2295"
## [2296] "V2296" "V2297" "V2298" "V2299" "V2300" "V2301" "V2302" "V2303" "V2304"
## [2305] "V2305" "V2306" "V2307" "V2308" "V2309" "V2310" "V2311" "V2312" "V2313"
## [2314] "V2314" "V2315" "V2316" "V2317" "V2318" "V2319" "V2320" "V2321" "V2322"
## [2323] "V2323" "V2324" "V2325" "V2326" "V2327" "V2328" "V2329" "V2330" "V2331"
## [2332] "V2332" "V2333" "V2334" "V2335" "V2336" "V2337" "V2338" "V2339" "V2340"
## [2341] "V2341" "V2342" "V2343" "V2344" "V2345" "V2346" "V2347" "V2348" "V2349"
## [2350] "V2350" "V2351" "V2352" "V2353" "V2354" "V2355" "V2356" "V2357" "V2358"
## [2359] "V2359" "V2360" "V2361" "V2362" "V2363" "V2364" "V2365" "V2366" "V2367"
## [2368] "V2368" "V2369" "V2370" "V2371" "V2372" "V2373" "V2374" "V2375" "V2376"
## [2377] "V2377" "V2378" "V2379" "V2380" "V2381" "V2382" "V2383" "V2384" "V2385"
## [2386] "V2386" "V2387" "V2388" "V2389" "V2390" "V2391" "V2392" "V2393" "V2394"
## [2395] "V2395" "V2396" "V2397" "V2398" "V2399" "V2400" "V2401" "V2402" "V2403"
## [2404] "V2404" "V2405" "V2406" "V2407" "V2408" "V2409" "V2410" "V2411" "V2412"
## [2413] "V2413" "V2414" "V2415" "V2416" "V2417" "V2418" "V2419" "V2420" "V2421"
## [2422] "V2422" "V2423" "V2424" "V2425" "V2426" "V2427" "V2428" "V2429" "V2430"
## [2431] "V2431" "V2432" "V2433" "V2434" "V2435" "V2436" "V2437" "V2438" "V2439"
## [2440] "V2440" "V2441" "V2442" "V2443" "V2444" "V2445" "V2446" "V2447" "V2448"
## [2449] "V2449" "V2450" "V2451" "V2452" "V2453" "V2454" "V2455" "V2456" "V2457"
## [2458] "V2458" "V2459" "V2460" "V2461" "V2462" "V2463" "V2464" "V2465" "V2466"
## [2467] "V2467" "V2468" "V2469" "V2470" "V2471" "V2472" "V2473" "V2474" "V2475"
## [2476] "V2476" "V2477" "V2478" "V2479" "V2480" "V2481" "V2482" "V2483" "V2484"
## [2485] "V2485" "V2486" "V2487" "V2488" "V2489" "V2490" "V2491" "V2492" "V2493"
## [2494] "V2494" "V2495" "V2496" "V2497" "V2498" "V2499" "V2500" "V2501" "V2502"
## [2503] "V2503" "V2504" "V2505" "V2506" "V2507" "V2508" "V2509" "V2510" "V2511"
## [2512] "V2512" "V2513" "V2514" "V2515" "V2516" "V2517" "V2518" "V2519" "V2520"
## [2521] "V2521" "V2522" "V2523" "V2524" "V2525" "V2526" "V2527" "V2528" "V2529"
## [2530] "V2530" "V2531" "V2532" "V2533" "V2534" "V2535" "V2536" "V2537" "V2538"
## [2539] "V2539" "V2540" "V2541" "V2542" "V2543" "V2544" "V2545" "V2546" "V2547"
## [2548] "V2548" "V2549" "V2550" "V2551" "V2552" "V2553" "V2554" "V2555" "V2556"
## [2557] "V2557" "V2558" "V2559" "V2560" "V2561" "V2562" "V2563" "V2564" "V2565"
## [2566] "V2566" "V2567" "V2568" "V2569" "V2570" "V2571" "V2572" "V2573" "V2574"
## [2575] "V2575" "V2576" "V2577" "V2578" "V2579" "V2580" "V2581" "V2582" "V2583"
## [2584] "V2584" "V2585" "V2586" "V2587" "V2588" "V2589" "V2590" "V2591" "V2592"
## [2593] "V2593" "V2594" "V2595" "V2596" "V2597" "V2598" "V2599" "V2600" "V2601"
## [2602] "V2602" "V2603" "V2604" "V2605" "V2606" "V2607" "V2608" "V2609" "V2610"
## [2611] "V2611" "V2612" "V2613" "V2614" "V2615" "V2616" "V2617" "V2618" "V2619"
## [2620] "V2620" "V2621" "V2622" "V2623" "V2624" "V2625" "V2626" "V2627" "V2628"
## [2629] "V2629" "V2630" "V2631" "V2632" "V2633" "V2634" "V2635" "V2636" "V2637"
## [2638] "V2638" "V2639" "V2640" "V2641" "V2642" "V2643" "V2644" "V2645" "V2646"
## [2647] "V2647" "V2648" "V2649" "V2650" "V2651" "V2652" "V2653" "V2654" "V2655"
## [2656] "V2656" "V2657" "V2658" "V2659" "V2660" "V2661" "V2662" "V2663" "V2664"
## [2665] "V2665" "V2666" "V2667" "V2668" "V2669" "V2670" "V2671" "V2672" "V2673"
## [2674] "V2674" "V2675" "V2676" "V2677" "V2678" "V2679" "V2680" "V2681" "V2682"
## [2683] "V2683" "V2684" "V2685" "V2686" "V2687" "V2688" "V2689" "V2690" "V2691"
## [2692] "V2692" "V2693" "V2694" "V2695" "V2696" "V2697" "V2698" "V2699" "V2700"
## [2701] "V2701" "V2702" "V2703" "V2704" "V2705" "V2706" "V2707" "V2708" "V2709"
## [2710] "V2710" "V2711" "V2712" "V2713" "V2714" "V2715" "V2716" "V2717" "V2718"
## [2719] "V2719" "V2720" "V2721" "V2722" "V2723" "V2724" "V2725" "V2726" "V2727"
## [2728] "V2728" "V2729" "V2730" "V2731" "V2732" "V2733" "V2734" "V2735" "V2736"
## [2737] "V2737" "V2738" "V2739" "V2740" "V2741" "V2742" "V2743" "V2744" "V2745"
## [2746] "V2746" "V2747" "V2748" "V2749" "V2750" "V2751" "V2752" "V2753" "V2754"
## [2755] "V2755" "V2756" "V2757" "V2758" "V2759" "V2760" "V2761" "V2762" "V2763"
## [2764] "V2764" "V2765" "V2766" "V2767" "V2768" "V2769" "V2770" "V2771" "V2772"
## [2773] "V2773" "V2774" "V2775" "V2776" "V2777" "V2778" "V2779" "V2780" "V2781"
## [2782] "V2782" "V2783" "V2784" "V2785" "V2786" "V2787" "V2788" "V2789" "V2790"
## [2791] "V2791" "V2792" "V2793" "V2794" "V2795" "V2796" "V2797" "V2798" "V2799"
## [2800] "V2800" "V2801" "V2802" "V2803" "V2804" "V2805" "V2806" "V2807" "V2808"
## [2809] "V2809" "V2810" "V2811" "V2812" "V2813" "V2814" "V2815" "V2816" "V2817"
## [2818] "V2818" "V2819" "V2820" "V2821" "V2822" "V2823" "V2824" "V2825" "V2826"
## [2827] "V2827" "V2828" "V2829" "V2830" "V2831" "V2832" "V2833" "V2834" "V2835"
## [2836] "V2836" "V2837" "V2838" "V2839" "V2840" "V2841" "V2842" "V2843" "V2844"
## [2845] "V2845" "V2846" "V2847" "V2848" "V2849" "V2850" "V2851" "V2852" "V2853"
## [2854] "V2854" "V2855" "V2856" "V2857" "V2858" "V2859" "V2860" "V2861" "V2862"
## [2863] "V2863" "V2864" "V2865" "V2866" "V2867" "V2868" "V2869" "V2870" "V2871"
## [2872] "V2872" "V2873" "V2874" "V2875" "V2876" "V2877" "V2878" "V2879" "V2880"
## [2881] "V2881" "V2882" "V2883" "V2884" "V2885" "V2886" "V2887" "V2888" "V2889"
## [2890] "V2890" "V2891" "V2892" "V2893" "V2894" "V2895" "V2896" "V2897" "V2898"
## [2899] "V2899" "V2900" "V2901" "V2902" "V2903" "V2904" "V2905" "V2906" "V2907"
## [2908] "V2908" "V2909" "V2910" "V2911" "V2912" "V2913" "V2914" "V2915" "V2916"
## [2917] "V2917" "V2918" "V2919" "V2920" "V2921" "V2922" "V2923" "V2924" "V2925"
## [2926] "V2926" "V2927" "V2928" "V2929" "V2930" "V2931" "V2932" "V2933" "V2934"
## [2935] "V2935" "V2936" "V2937" "V2938" "V2939" "V2940" "V2941" "V2942" "V2943"
## [2944] "V2944" "V2945" "V2946" "V2947" "V2948" "V2949" "V2950" "V2951" "V2952"
## [2953] "V2953" "V2954" "V2955" "V2956" "V2957" "V2958" "V2959" "V2960" "V2961"
## [2962] "V2962" "V2963" "V2964" "V2965" "V2966" "V2967" "V2968" "V2969" "V2970"
## [2971] "V2971" "V2972" "V2973" "V2974" "V2975" "V2976" "V2977" "V2978" "V2979"
## [2980] "V2980" "V2981" "V2982" "V2983" "V2984" "V2985" "V2986" "V2987" "V2988"
## [2989] "V2989" "V2990" "V2991" "V2992" "V2993" "V2994" "V2995" "V2996" "V2997"
## [2998] "V2998" "V2999" "V3000" "V3001" "V3002" "V3003" "V3004" "V3005" "V3006"
## [3007] "V3007" "V3008" "V3009" "V3010" "V3011" "V3012" "V3013" "V3014" "V3015"
## [3016] "V3016" "V3017" "V3018" "V3019" "V3020" "V3021" "V3022" "V3023" "V3024"
## [3025] "V3025" "V3026" "V3027" "V3028" "V3029" "V3030" "V3031" "V3032" "V3033"
## [3034] "V3034" "V3035" "V3036" "V3037" "V3038" "V3039" "V3040" "V3041" "V3042"
## [3043] "V3043" "V3044" "V3045" "V3046" "V3047" "V3048" "V3049" "V3050" "V3051"
## [3052] "V3052" "V3053" "V3054" "V3055" "V3056" "V3057" "V3058" "V3059" "V3060"
## [3061] "V3061" "V3062" "V3063" "V3064" "V3065" "V3066" "V3067" "V3068" "V3069"
## [3070] "V3070" "V3071" "V3072" "V3073" "V3074" "V3075" "V3076" "V3077" "V3078"
## [3079] "V3079" "V3080" "V3081" "V3082" "V3083" "V3084" "V3085" "V3086" "V3087"
## [3088] "V3088" "V3089" "V3090" "V3091" "V3092" "V3093" "V3094" "V3095" "V3096"
## [3097] "V3097" "V3098" "V3099" "V3100" "V3101" "V3102" "V3103" "V3104" "V3105"
## [3106] "V3106" "V3107" "V3108" "V3109" "V3110" "V3111" "V3112" "V3113" "V3114"
## [3115] "V3115" "V3116" "V3117" "V3118" "V3119" "V3120" "V3121" "V3122" "V3123"
## [3124] "V3124" "V3125" "V3126" "V3127" "V3128" "V3129" "V3130" "V3131" "V3132"
## [3133] "V3133" "V3134" "V3135" "V3136" "V3137" "V3138" "V3139" "V3140" "V3141"
## [3142] "V3142" "V3143" "V3144" "V3145" "V3146" "V3147" "V3148" "V3149" "V3150"
## [3151] "V3151" "V3152" "V3153" "V3154" "V3155" "V3156" "V3157" "V3158" "V3159"
## [3160] "V3160" "V3161" "V3162" "V3163" "V3164" "V3165" "V3166" "V3167" "V3168"
## [3169] "V3169" "V3170" "V3171" "V3172" "V3173" "V3174" "V3175" "V3176" "V3177"
## [3178] "V3178" "V3179" "V3180" "V3181" "V3182" "V3183" "V3184" "V3185" "V3186"
## [3187] "V3187" "V3188" "V3189" "V3190" "V3191" "V3192" "V3193" "V3194" "V3195"
## [3196] "V3196" "V3197" "V3198" "V3199" "V3200" "V3201" "V3202" "V3203" "V3204"
## [3205] "V3205" "V3206" "V3207" "V3208" "V3209" "V3210" "V3211" "V3212" "V3213"
## [3214] "V3214" "V3215" "V3216" "V3217" "V3218" "V3219" "V3220" "V3221" "V3222"
## [3223] "V3223" "V3224" "V3225" "V3226" "V3227" "V3228" "V3229" "V3230" "V3231"
## [3232] "V3232" "V3233" "V3234" "V3235" "V3236" "V3237" "V3238" "V3239" "V3240"
## [3241] "V3241" "V3242" "V3243" "V3244" "V3245" "V3246" "V3247" "V3248" "V3249"
## [3250] "V3250" "V3251" "V3252" "V3253" "V3254" "V3255" "V3256" "V3257" "V3258"
## [3259] "V3259" "V3260" "V3261" "V3262" "V3263" "V3264" "V3265" "V3266" "V3267"
## [3268] "V3268" "V3269" "V3270" "V3271" "V3272" "V3273" "V3274" "V3275" "V3276"
## [3277] "V3277" "V3278" "V3279" "V3280" "V3281" "V3282" "V3283" "V3284" "V3285"
## [3286] "V3286" "V3287" "V3288" "V3289" "V3290" "V3291" "V3292" "V3293" "V3294"
## [3295] "V3295" "V3296" "V3297" "V3298" "V3299" "V3300" "V3301" "V3302" "V3303"
## [3304] "V3304" "V3305" "V3306" "V3307" "V3308" "V3309" "V3310" "V3311" "V3312"
## [3313] "V3313" "V3314" "V3315" "V3316" "V3317" "V3318" "V3319" "V3320" "V3321"
## [3322] "V3322" "V3323" "V3324" "V3325" "V3326" "V3327" "V3328" "V3329" "V3330"
## [3331] "V3331" "V3332" "V3333" "V3334" "V3335" "V3336" "V3337" "V3338" "V3339"
## [3340] "V3340" "V3341" "V3342" "V3343" "V3344" "V3345" "V3346" "V3347" "V3348"
## [3349] "V3349" "V3350" "V3351" "V3352" "V3353" "V3354" "V3355" "V3356" "V3357"
## [3358] "V3358" "V3359" "V3360" "V3361" "V3362" "V3363" "V3364" "V3365" "V3366"
## [3367] "V3367" "V3368" "V3369" "V3370" "V3371" "V3372" "V3373" "V3374" "V3375"
## [3376] "V3376" "V3377" "V3378" "V3379" "V3380" "V3381" "V3382" "V3383" "V3384"
## [3385] "V3385" "V3386" "V3387" "V3388" "V3389" "V3390" "V3391" "V3392" "V3393"
## [3394] "V3394" "V3395" "V3396" "V3397" "V3398" "V3399" "V3400" "V3401" "V3402"
## [3403] "V3403" "V3404" "V3405" "V3406" "V3407" "V3408" "V3409" "V3410" "V3411"
## [3412] "V3412" "V3413" "V3414" "V3415" "V3416" "V3417" "V3418" "V3419" "V3420"
## [3421] "V3421" "V3422" "V3423" "V3424" "V3425" "V3426" "V3427" "V3428" "V3429"
## [3430] "V3430" "V3431" "V3432" "V3433" "V3434" "V3435" "V3436" "V3437" "V3438"
## [3439] "V3439" "V3440" "V3441" "V3442" "V3443" "V3444" "V3445" "V3446" "V3447"
## [3448] "V3448" "V3449" "V3450" "V3451" "V3452" "V3453" "V3454" "V3455" "V3456"
## [3457] "V3457" "V3458" "V3459" "V3460" "V3461" "V3462" "V3463" "V3464" "V3465"
## [3466] "V3466" "V3467" "V3468" "V3469" "V3470" "V3471" "V3472" "V3473" "V3474"
## [3475] "V3475" "V3476" "V3477" "V3478" "V3479" "V3480" "V3481" "V3482" "V3483"
## [3484] "V3484" "V3485" "V3486" "V3487" "V3488" "V3489" "V3490" "V3491" "V3492"
## [3493] "V3493" "V3494" "V3495" "V3496" "V3497" "V3498" "V3499" "V3500" "V3501"
## [3502] "V3502" "V3503" "V3504" "V3505" "V3506" "V3507" "V3508" "V3509" "V3510"
## [3511] "V3511" "V3512" "V3513" "V3514" "V3515" "V3516" "V3517" "V3518" "V3519"
## [3520] "V3520" "V3521" "V3522" "V3523" "V3524" "V3525" "V3526" "V3527" "V3528"
## [3529] "V3529" "V3530" "V3531" "V3532" "V3533" "V3534" "V3535" "V3536" "V3537"
## [3538] "V3538" "V3539" "V3540" "V3541" "V3542" "V3543" "V3544" "V3545" "V3546"
## [3547] "V3547" "V3548" "V3549" "V3550" "V3551" "V3552" "V3553" "V3554" "V3555"
## [3556] "V3556" "V3557" "V3558" "V3559" "V3560" "V3561" "V3562" "V3563" "V3564"
## [3565] "V3565" "V3566" "V3567" "V3568" "V3569" "V3570" "V3571" "V3572" "V3573"
## [3574] "V3574" "V3575" "V3576" "V3577" "V3578" "V3579" "V3580" "V3581" "V3582"
## [3583] "V3583" "V3584" "V3585" "V3586" "V3587" "V3588" "V3589" "V3590" "V3591"
## [3592] "V3592" "V3593" "V3594" "V3595" "V3596" "V3597" "V3598" "V3599" "V3600"
## [3601] "V3601" "V3602" "V3603" "V3604" "V3605" "V3606" "V3607" "V3608" "V3609"
## [3610] "V3610" "V3611" "V3612" "V3613" "V3614" "V3615" "V3616" "V3617" "V3618"
## [3619] "V3619" "V3620" "V3621" "V3622" "V3623" "V3624" "V3625" "V3626" "V3627"
## [3628] "V3628" "V3629" "V3630" "V3631" "V3632" "V3633" "V3634" "V3635" "V3636"
## [3637] "V3637" "V3638" "V3639" "V3640" "V3641" "V3642" "V3643" "V3644" "V3645"
## [3646] "V3646" "V3647" "V3648" "V3649" "V3650" "V3651" "V3652" "V3653" "V3654"
## [3655] "V3655" "V3656" "V3657" "V3658" "V3659" "V3660" "V3661" "V3662" "V3663"
## [3664] "V3664" "V3665" "V3666" "V3667" "V3668" "V3669" "V3670" "V3671" "V3672"
## [3673] "V3673" "V3674" "V3675" "V3676" "V3677" "V3678" "V3679" "V3680" "V3681"
## [3682] "V3682" "V3683" "V3684" "V3685" "V3686" "V3687" "V3688" "V3689" "V3690"
## [3691] "V3691" "V3692" "V3693" "V3694" "V3695" "V3696" "V3697" "V3698" "V3699"
## [3700] "V3700" "V3701" "V3702" "V3703" "V3704" "V3705" "V3706" "V3707" "V3708"
## [3709] "V3709" "V3710" "V3711" "V3712" "V3713" "V3714" "V3715" "V3716" "V3717"
## [3718] "V3718" "V3719" "V3720" "V3721" "V3722" "V3723" "V3724" "V3725" "V3726"
## [3727] "V3727" "V3728" "V3729" "V3730" "V3731" "V3732" "V3733" "V3734" "V3735"
## [3736] "V3736" "V3737" "V3738" "V3739" "V3740" "V3741" "V3742" "V3743" "V3744"
## [3745] "V3745" "V3746" "V3747" "V3748" "V3749" "V3750" "V3751" "V3752" "V3753"
## [3754] "V3754" "V3755" "V3756" "V3757" "V3758" "V3759" "V3760" "V3761" "V3762"
## [3763] "V3763" "V3764" "V3765" "V3766" "V3767" "V3768" "V3769" "V3770" "V3771"
## [3772] "V3772" "V3773" "V3774" "V3775" "V3776" "V3777" "V3778" "V3779" "V3780"
## [3781] "V3781" "V3782" "V3783" "V3784" "V3785" "V3786" "V3787" "V3788" "V3789"
## [3790] "V3790" "V3791" "V3792" "V3793" "V3794" "V3795" "V3796" "V3797" "V3798"
## [3799] "V3799" "V3800" "V3801" "V3802" "V3803" "V3804" "V3805" "V3806" "V3807"
## [3808] "V3808" "V3809" "V3810" "V3811" "V3812" "V3813" "V3814" "V3815" "V3816"
## [3817] "V3817" "V3818" "V3819" "V3820" "V3821" "V3822" "V3823" "V3824" "V3825"
## [3826] "V3826" "V3827" "V3828" "V3829" "V3830" "V3831" "V3832" "V3833" "V3834"
## [3835] "V3835" "V3836" "V3837" "V3838" "V3839" "V3840" "V3841" "V3842" "V3843"
## [3844] "V3844" "V3845" "V3846" "V3847" "V3848" "V3849" "V3850" "V3851" "V3852"
## [3853] "V3853" "V3854" "V3855" "V3856" "V3857" "V3858" "V3859" "V3860" "V3861"
## [3862] "V3862" "V3863" "V3864" "V3865" "V3866" "V3867" "V3868" "V3869" "V3870"
## [3871] "V3871" "V3872" "V3873" "V3874" "V3875" "V3876" "V3877" "V3878" "V3879"
## [3880] "V3880" "V3881" "V3882" "V3883" "V3884" "V3885" "V3886" "V3887" "V3888"
## [3889] "V3889" "V3890" "V3891" "V3892" "V3893" "V3894" "V3895" "V3896" "V3897"
## [3898] "V3898" "V3899" "V3900" "V3901" "V3902" "V3903" "V3904" "V3905" "V3906"
## [3907] "V3907" "V3908" "V3909" "V3910" "V3911" "V3912" "V3913" "V3914" "V3915"
## [3916] "V3916" "V3917" "V3918" "V3919" "V3920" "V3921" "V3922" "V3923" "V3924"
## [3925] "V3925" "V3926" "V3927" "V3928" "V3929" "V3930" "V3931" "V3932" "V3933"
## [3934] "V3934" "V3935" "V3936" "V3937" "V3938" "V3939" "V3940" "V3941" "V3942"
## [3943] "V3943" "V3944" "V3945" "V3946" "V3947" "V3948" "V3949" "V3950" "V3951"
## [3952] "V3952" "V3953" "V3954" "V3955" "V3956" "V3957" "V3958" "V3959" "V3960"
## [3961] "V3961" "V3962" "V3963" "V3964" "V3965" "V3966" "V3967" "V3968" "V3969"
## [3970] "V3970" "V3971" "V3972" "V3973" "V3974" "V3975" "V3976" "V3977" "V3978"
## [3979] "V3979" "V3980" "V3981" "V3982" "V3983" "V3984" "V3985" "V3986" "V3987"
## [3988] "V3988" "V3989" "V3990" "V3991" "V3992" "V3993" "V3994" "V3995" "V3996"
## [3997] "V3997" "V3998" "V3999" "V4000"
##
## $class
## [1] "data.frame"
##
## $row.names
## [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
## [19] 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
## [37] 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54
## [55] 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72
## [73] 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90
## [91] 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108
## [109] 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126
## [127] 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144
## [145] 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162
## [163] 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180
## [181] 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198
## [199] 199 200# las filas son el número de puntos de evaluación de la función y las columnas el número de curvas
# Suavizamiento spline
# Creación de la base de funciones
npuntos <- nrow(imagenductilxeydf)
base_bspline <- create.bspline.basis(c(1, npuntos), 150)
plot(base_bspline)
summary(base_bspline)##
## Basis object:
##
## Type: bspline
##
## Range: 1 to 200
##
## Number of basis functions: 150# Selección de lambda
gcv <- NULL
lambda_list <- seq(-2, 4, length.out = 30)
# estos son las potencias de 10 de variación del lambda
# inicia con valores muy cercanos a cero 10^-2 hasta 10^4
matrix_data <- as.matrix(imagenductilxeydf)
for (lambda in lambda_list) {
lambda <- 10**lambda
param_lambda <- fdPar(base_bspline,
2,
lambda)
fd_smoothductil <- smooth.basis(argvals = seq(1,
nrow(matrix_data)),
y = matrix_data,
fdParobj = param_lambda)
gcv <- c(gcv, sum(fd_smoothductil$gcv))
}
# Se esta tomando como criterio total la suma de las VC de todas las curvas
plotgcv <-
data.frame(log_lambda = lambda_list,
gcv = gcv) %>% ggplot(aes(x = log_lambda, y = gcv)) +
geom_line(color = "purple", linetype = "dashed") +
theme_light() +
scale_x_continuous(limits = c(0, 4))
plotly::ggplotly(plotgcv)selected_lamdba <- 10**lambda_list[which.min(gcv)]
print(selected_lamdba)## [1] 0.02592944print(log(selected_lamdba, 10))## [1] -1.586207# entrega el valor de lambda donde se minimiza la suma de VC y log de lambda
# Suavizamiento con el lambda elegido
param_lambda <- fdPar(base_bspline,
2,
lambda = selected_lamdba)
fd_smoothductil <- smooth.basis(argvals = seq(1,
nrow(matrix_data)),
y = matrix_data,
fdParobj = param_lambda)
plot(fd_smoothductil, xlab= "Pixel", ylab = "Intensidad Totas Las Imagenes")
## [1] "done"# una curva por cada foto
# Comparación de curvas originales y suavizadas
fd_fittedductil <- fitted(fd_smoothductil)
plot(imagenductilxey[,1],type = "o",xlab="Pixel",ylab="Intensidad Ent1")
lines(fd_fittedductil[,1],col="2")
plot(imagenductilxey[,401],type = "o",xlab="Pixel",ylab="Intensidad Ent2")
lines(fd_fittedductil[,401],col="2")
plot(imagenductilxey[,801],type = "o",xlab="Pixel",ylab="Intensidad Ent3")
lines(fd_fittedductil[,801],col="2")
plot(imagenductilxey[,1201],type = "o",xlab="Pixel",ylab="Intensidad Ent4")
lines(fd_fittedductil[,1201],col="2")
plot(imagenductilxey[,1601],type = "o",xlab="Pixel",ylab="Intensidad Ent5")
lines(fd_fittedductil[,1601],col="2")
plot(imagenductilxey[,2001],type = "o",xlab="Pixel",ylab="Intensidad Ent6")
lines(fd_fittedductil[,2001],col="2")
plot(imagenductilxey[,2401],type = "o",xlab="Pixel",ylab="Intensidad Ent7")
lines(fd_fittedductil[,2401],col="2")
plot(imagenductilxey[,2801],type = "o",xlab="Pixel",ylab="Intensidad Ens1")
lines(fd_fittedductil[,2801],col="2")
plot(imagenductilxey[,3201],type = "o",xlab="Pixel",ylab="Intensidad Ens2")
lines(fd_fittedductil[,3201],col="2")
plot(imagenductilxey[,3601],type = "o",xlab="Pixel",ylab="Intensidad Ens3")
lines(fd_fittedductil[,3601],col="2")
1.1 Función de varianza imagenes dúctiles
Para ello se usa la función var.fd. En este caso se divide el recorrido en 200 puntos (igual que los pixeles).
Se calcula el operador de los datos de entrenamiento como conjunto y el de cada imagen de ensayo por separado.
var_fdductilEnt <- var.fd(fd_smoothductil$fd[1:2800])
var_fdductilEns1 <- var.fd(fd_smoothductil$fd[2801:3200])
var_fdductilEns2 <- var.fd(fd_smoothductil$fd[3201:3600])
var_fdductilEns3 <- var.fd(fd_smoothductil$fd[3601:4000])
# Calcula la varianza del objeto funcional de cada imagen
# La salida es un objeto bivariado funcional
# Necesita dos bases una para cada eje
eva <- seq(1, npuntos, length = 200)
matriz_var_ductilEnt <- eval.bifd(eva, eva, var_fdductilEnt)
matriz_var_ductilEns1 <- eval.bifd(eva, eva, var_fdductilEns1)
matriz_var_ductilEns2 <- eval.bifd(eva, eva, var_fdductilEns2)
matriz_var_ductilEns3 <- eval.bifd(eva, eva, var_fdductilEns3)2. Cargar imagenes frágiles
Total de imagenes 10. Por cada foto 400 datos funcionales (lineas de pixeles en X y líneas de pixeles en y), para un total de 4000 datos.
imagenfragilent1 <- read.bitmap("FragilEnt1.jpg") # crea una matriz de x filas y columanas y z=3 canales
imagenfragilent1 <- imagenfragilent1 [,,1] # Deja un solo canal
imagenfragilent1t <- t(imagenfragilent1)
imagenfragilent1xey <- rbind(imagenfragilent1,imagenfragilent1t)
imagenfragilent1xey <- t(imagenfragilent1xey)
dim(imagenfragilent1xey)## [1] 200 400imagenfragilent2 <- read.bitmap("FragilEnt2.jpg") # crea una matriz de x filas y columanas y z=3 canales
imagenfragilent2 <- imagenfragilent2 [,,1] # Deja un solo canal
imagenfragilent2t <- t(imagenfragilent2)
imagenfragilent2xey <- rbind(imagenfragilent2,imagenfragilent2t)
imagenfragilent2xey <- t(imagenfragilent2xey)
dim(imagenfragilent2xey)## [1] 200 400imagenfragilent3 <- read.bitmap("FragilEnt3.jpg") # crea una matriz de x filas y columanas y z=3 canales
imagenfragilent3 <- imagenfragilent3 [,,1] # Deja un solo canal
imagenfragilent3t <- t(imagenfragilent3)
imagenfragilent3xey <- rbind(imagenfragilent3,imagenfragilent3t)
imagenfragilent3xey <- t(imagenfragilent3xey)
dim(imagenfragilent3xey)## [1] 200 400imagenfragilent4 <- read.bitmap("FragilEnt4.jpg") # crea una matriz de x filas y columanas y z=3 canales
imagenfragilent4 <- imagenfragilent4 [,,1] # Deja un solo canal
imagenfragilent4t <- t(imagenfragilent4)
imagenfragilent4xey <- rbind(imagenfragilent4,imagenfragilent4t)
imagenfragilent4xey <- t(imagenfragilent4xey)
dim(imagenfragilent4xey)## [1] 200 400imagenfragilent5 <- read.bitmap("FragilEnt5.jpg") # crea una matriz de x filas y columanas y z=3 canales
imagenfragilent5 <- imagenfragilent5 [,,1] # Deja un solo canal
imagenfragilent5t <- t(imagenfragilent5)
imagenfragilent5xey <- rbind(imagenfragilent5,imagenfragilent5t)
imagenfragilent5xey <- t(imagenfragilent5xey)
dim(imagenfragilent5xey)## [1] 200 400imagenfragilent6 <- read.bitmap("FragilEnt6.jpg") # crea una matriz de x filas y columanas y z=3 canales
imagenfragilent6 <- imagenfragilent6 [,,1] # Deja un solo canal
imagenfragilent6t <- t(imagenfragilent6)
imagenfragilent6xey <- rbind(imagenfragilent6,imagenfragilent6t)
imagenfragilent6xey <- t(imagenfragilent6xey)
dim(imagenfragilent6xey)## [1] 200 400imagenfragilent7 <- read.bitmap("FragilEnt7.jpg") # crea una matriz de x filas y columanas y z=3 canales
imagenfragilent7 <- imagenfragilent7 [,,1] # Deja un solo canal
imagenfragilent7t <- t(imagenfragilent7)
imagenfragilent7xey <- rbind(imagenfragilent7,imagenfragilent7t)
imagenfragilent7xey <- t(imagenfragilent7xey)
dim(imagenfragilent7xey)## [1] 200 400imagenfragilens1 <- read.bitmap("FragilEns1.jpg") # crea una matriz de x filas y columanas y z=3 canales
imagenfragilens1 <- imagenfragilens1 [,,1] # Deja un solo canal
imagenfragilens1t <- t(imagenfragilens1)
imagenfragilens1xey <- rbind(imagenfragilens1,imagenfragilens1t)
imagenfragilens1xey <- t(imagenfragilens1xey)
dim(imagenfragilens1xey)## [1] 200 400imagenfragilens2 <- read.bitmap("FragilEns2.jpg") # crea una matriz de x filas y columanas y z=3 canales
imagenfragilens2 <- imagenfragilens2 [,,1] # Deja un solo canal
imagenfragilens2t <- t(imagenfragilens2)
imagenfragilens2xey <- rbind(imagenfragilens2,imagenfragilens2t)
imagenfragilens2xey <- t(imagenfragilens2xey)
dim(imagenfragilens2xey)## [1] 200 400imagenfragilens3 <- read.bitmap("fragilEns3.jpg") # crea una matriz de x filas y columanas y z=3 canales
imagenfragilens3 <- imagenfragilens3 [,,1] # Deja un solo canal
imagenfragilens3t <- t(imagenfragilens3)
imagenfragilens3xey <- rbind(imagenfragilens3,imagenfragilens3t)
imagenfragilens3xey <- t(imagenfragilens3xey)
dim(imagenfragilens3xey)## [1] 200 400imagenfragilxey <- cbind(imagenfragilent1xey,imagenfragilent2xey,imagenfragilent3xey,imagenfragilent4xey,imagenfragilent5xey,imagenfragilent6xey,imagenfragilent7xey,imagenfragilens1xey,imagenfragilens2xey,imagenfragilens3xey)
dim(imagenfragilxey)## [1] 200 4000# Convertir en Data Frame fragil
imagenfragilxeydf <- as.data.frame (imagenfragilxey)
attributes(imagenfragilxeydf)## $names
## [1] "V1" "V2" "V3" "V4" "V5" "V6" "V7" "V8" "V9"
## [10] "V10" "V11" "V12" "V13" "V14" "V15" "V16" "V17" "V18"
## [19] "V19" "V20" "V21" "V22" "V23" "V24" "V25" "V26" "V27"
## [28] "V28" "V29" "V30" "V31" "V32" "V33" "V34" "V35" "V36"
## [37] "V37" "V38" "V39" "V40" "V41" "V42" "V43" "V44" "V45"
## [46] "V46" "V47" "V48" "V49" "V50" "V51" "V52" "V53" "V54"
## [55] "V55" "V56" "V57" "V58" "V59" "V60" "V61" "V62" "V63"
## [64] "V64" "V65" "V66" "V67" "V68" "V69" "V70" "V71" "V72"
## [73] "V73" "V74" "V75" "V76" "V77" "V78" "V79" "V80" "V81"
## [82] "V82" "V83" "V84" "V85" "V86" "V87" "V88" "V89" "V90"
## [91] "V91" "V92" "V93" "V94" "V95" "V96" "V97" "V98" "V99"
## [100] "V100" "V101" "V102" "V103" "V104" "V105" "V106" "V107" "V108"
## [109] "V109" "V110" "V111" "V112" "V113" "V114" "V115" "V116" "V117"
## [118] "V118" "V119" "V120" "V121" "V122" "V123" "V124" "V125" "V126"
## [127] "V127" "V128" "V129" "V130" "V131" "V132" "V133" "V134" "V135"
## [136] "V136" "V137" "V138" "V139" "V140" "V141" "V142" "V143" "V144"
## [145] "V145" "V146" "V147" "V148" "V149" "V150" "V151" "V152" "V153"
## [154] "V154" "V155" "V156" "V157" "V158" "V159" "V160" "V161" "V162"
## [163] "V163" "V164" "V165" "V166" "V167" "V168" "V169" "V170" "V171"
## [172] "V172" "V173" "V174" "V175" "V176" "V177" "V178" "V179" "V180"
## [181] "V181" "V182" "V183" "V184" "V185" "V186" "V187" "V188" "V189"
## [190] "V190" "V191" "V192" "V193" "V194" "V195" "V196" "V197" "V198"
## [199] "V199" "V200" "V201" "V202" "V203" "V204" "V205" "V206" "V207"
## [208] "V208" "V209" "V210" "V211" "V212" "V213" "V214" "V215" "V216"
## [217] "V217" "V218" "V219" "V220" "V221" "V222" "V223" "V224" "V225"
## [226] "V226" "V227" "V228" "V229" "V230" "V231" "V232" "V233" "V234"
## [235] "V235" "V236" "V237" "V238" "V239" "V240" "V241" "V242" "V243"
## [244] "V244" "V245" "V246" "V247" "V248" "V249" "V250" "V251" "V252"
## [253] "V253" "V254" "V255" "V256" "V257" "V258" "V259" "V260" "V261"
## [262] "V262" "V263" "V264" "V265" "V266" "V267" "V268" "V269" "V270"
## [271] "V271" "V272" "V273" "V274" "V275" "V276" "V277" "V278" "V279"
## [280] "V280" "V281" "V282" "V283" "V284" "V285" "V286" "V287" "V288"
## [289] "V289" "V290" "V291" "V292" "V293" "V294" "V295" "V296" "V297"
## [298] "V298" "V299" "V300" "V301" "V302" "V303" "V304" "V305" "V306"
## [307] "V307" "V308" "V309" "V310" "V311" "V312" "V313" "V314" "V315"
## [316] "V316" "V317" "V318" "V319" "V320" "V321" "V322" "V323" "V324"
## [325] "V325" "V326" "V327" "V328" "V329" "V330" "V331" "V332" "V333"
## [334] "V334" "V335" "V336" "V337" "V338" "V339" "V340" "V341" "V342"
## [343] "V343" "V344" "V345" "V346" "V347" "V348" "V349" "V350" "V351"
## [352] "V352" "V353" "V354" "V355" "V356" "V357" "V358" "V359" "V360"
## [361] "V361" "V362" "V363" "V364" "V365" "V366" "V367" "V368" "V369"
## [370] "V370" "V371" "V372" "V373" "V374" "V375" "V376" "V377" "V378"
## [379] "V379" "V380" "V381" "V382" "V383" "V384" "V385" "V386" "V387"
## [388] "V388" "V389" "V390" "V391" "V392" "V393" "V394" "V395" "V396"
## [397] "V397" "V398" "V399" "V400" "V401" "V402" "V403" "V404" "V405"
## [406] "V406" "V407" "V408" "V409" "V410" "V411" "V412" "V413" "V414"
## [415] "V415" "V416" "V417" "V418" "V419" "V420" "V421" "V422" "V423"
## [424] "V424" "V425" "V426" "V427" "V428" "V429" "V430" "V431" "V432"
## [433] "V433" "V434" "V435" "V436" "V437" "V438" "V439" "V440" "V441"
## [442] "V442" "V443" "V444" "V445" "V446" "V447" "V448" "V449" "V450"
## [451] "V451" "V452" "V453" "V454" "V455" "V456" "V457" "V458" "V459"
## [460] "V460" "V461" "V462" "V463" "V464" "V465" "V466" "V467" "V468"
## [469] "V469" "V470" "V471" "V472" "V473" "V474" "V475" "V476" "V477"
## [478] "V478" "V479" "V480" "V481" "V482" "V483" "V484" "V485" "V486"
## [487] "V487" "V488" "V489" "V490" "V491" "V492" "V493" "V494" "V495"
## [496] "V496" "V497" "V498" "V499" "V500" "V501" "V502" "V503" "V504"
## [505] "V505" "V506" "V507" "V508" "V509" "V510" "V511" "V512" "V513"
## [514] "V514" "V515" "V516" "V517" "V518" "V519" "V520" "V521" "V522"
## [523] "V523" "V524" "V525" "V526" "V527" "V528" "V529" "V530" "V531"
## [532] "V532" "V533" "V534" "V535" "V536" "V537" "V538" "V539" "V540"
## [541] "V541" "V542" "V543" "V544" "V545" "V546" "V547" "V548" "V549"
## [550] "V550" "V551" "V552" "V553" "V554" "V555" "V556" "V557" "V558"
## [559] "V559" "V560" "V561" "V562" "V563" "V564" "V565" "V566" "V567"
## [568] "V568" "V569" "V570" "V571" "V572" "V573" "V574" "V575" "V576"
## [577] "V577" "V578" "V579" "V580" "V581" "V582" "V583" "V584" "V585"
## [586] "V586" "V587" "V588" "V589" "V590" "V591" "V592" "V593" "V594"
## [595] "V595" "V596" "V597" "V598" "V599" "V600" "V601" "V602" "V603"
## [604] "V604" "V605" "V606" "V607" "V608" "V609" "V610" "V611" "V612"
## [613] "V613" "V614" "V615" "V616" "V617" "V618" "V619" "V620" "V621"
## [622] "V622" "V623" "V624" "V625" "V626" "V627" "V628" "V629" "V630"
## [631] "V631" "V632" "V633" "V634" "V635" "V636" "V637" "V638" "V639"
## [640] "V640" "V641" "V642" "V643" "V644" "V645" "V646" "V647" "V648"
## [649] "V649" "V650" "V651" "V652" "V653" "V654" "V655" "V656" "V657"
## [658] "V658" "V659" "V660" "V661" "V662" "V663" "V664" "V665" "V666"
## [667] "V667" "V668" "V669" "V670" "V671" "V672" "V673" "V674" "V675"
## [676] "V676" "V677" "V678" "V679" "V680" "V681" "V682" "V683" "V684"
## [685] "V685" "V686" "V687" "V688" "V689" "V690" "V691" "V692" "V693"
## [694] "V694" "V695" "V696" "V697" "V698" "V699" "V700" "V701" "V702"
## [703] "V703" "V704" "V705" "V706" "V707" "V708" "V709" "V710" "V711"
## [712] "V712" "V713" "V714" "V715" "V716" "V717" "V718" "V719" "V720"
## [721] "V721" "V722" "V723" "V724" "V725" "V726" "V727" "V728" "V729"
## [730] "V730" "V731" "V732" "V733" "V734" "V735" "V736" "V737" "V738"
## [739] "V739" "V740" "V741" "V742" "V743" "V744" "V745" "V746" "V747"
## [748] "V748" "V749" "V750" "V751" "V752" "V753" "V754" "V755" "V756"
## [757] "V757" "V758" "V759" "V760" "V761" "V762" "V763" "V764" "V765"
## [766] "V766" "V767" "V768" "V769" "V770" "V771" "V772" "V773" "V774"
## [775] "V775" "V776" "V777" "V778" "V779" "V780" "V781" "V782" "V783"
## [784] "V784" "V785" "V786" "V787" "V788" "V789" "V790" "V791" "V792"
## [793] "V793" "V794" "V795" "V796" "V797" "V798" "V799" "V800" "V801"
## [802] "V802" "V803" "V804" "V805" "V806" "V807" "V808" "V809" "V810"
## [811] "V811" "V812" "V813" "V814" "V815" "V816" "V817" "V818" "V819"
## [820] "V820" "V821" "V822" "V823" "V824" "V825" "V826" "V827" "V828"
## [829] "V829" "V830" "V831" "V832" "V833" "V834" "V835" "V836" "V837"
## [838] "V838" "V839" "V840" "V841" "V842" "V843" "V844" "V845" "V846"
## [847] "V847" "V848" "V849" "V850" "V851" "V852" "V853" "V854" "V855"
## [856] "V856" "V857" "V858" "V859" "V860" "V861" "V862" "V863" "V864"
## [865] "V865" "V866" "V867" "V868" "V869" "V870" "V871" "V872" "V873"
## [874] "V874" "V875" "V876" "V877" "V878" "V879" "V880" "V881" "V882"
## [883] "V883" "V884" "V885" "V886" "V887" "V888" "V889" "V890" "V891"
## [892] "V892" "V893" "V894" "V895" "V896" "V897" "V898" "V899" "V900"
## [901] "V901" "V902" "V903" "V904" "V905" "V906" "V907" "V908" "V909"
## [910] "V910" "V911" "V912" "V913" "V914" "V915" "V916" "V917" "V918"
## [919] "V919" "V920" "V921" "V922" "V923" "V924" "V925" "V926" "V927"
## [928] "V928" "V929" "V930" "V931" "V932" "V933" "V934" "V935" "V936"
## [937] "V937" "V938" "V939" "V940" "V941" "V942" "V943" "V944" "V945"
## [946] "V946" "V947" "V948" "V949" "V950" "V951" "V952" "V953" "V954"
## [955] "V955" "V956" "V957" "V958" "V959" "V960" "V961" "V962" "V963"
## [964] "V964" "V965" "V966" "V967" "V968" "V969" "V970" "V971" "V972"
## [973] "V973" "V974" "V975" "V976" "V977" "V978" "V979" "V980" "V981"
## [982] "V982" "V983" "V984" "V985" "V986" "V987" "V988" "V989" "V990"
## [991] "V991" "V992" "V993" "V994" "V995" "V996" "V997" "V998" "V999"
## [1000] "V1000" "V1001" "V1002" "V1003" "V1004" "V1005" "V1006" "V1007" "V1008"
## [1009] "V1009" "V1010" "V1011" "V1012" "V1013" "V1014" "V1015" "V1016" "V1017"
## [1018] "V1018" "V1019" "V1020" "V1021" "V1022" "V1023" "V1024" "V1025" "V1026"
## [1027] "V1027" "V1028" "V1029" "V1030" "V1031" "V1032" "V1033" "V1034" "V1035"
## [1036] "V1036" "V1037" "V1038" "V1039" "V1040" "V1041" "V1042" "V1043" "V1044"
## [1045] "V1045" "V1046" "V1047" "V1048" "V1049" "V1050" "V1051" "V1052" "V1053"
## [1054] "V1054" "V1055" "V1056" "V1057" "V1058" "V1059" "V1060" "V1061" "V1062"
## [1063] "V1063" "V1064" "V1065" "V1066" "V1067" "V1068" "V1069" "V1070" "V1071"
## [1072] "V1072" "V1073" "V1074" "V1075" "V1076" "V1077" "V1078" "V1079" "V1080"
## [1081] "V1081" "V1082" "V1083" "V1084" "V1085" "V1086" "V1087" "V1088" "V1089"
## [1090] "V1090" "V1091" "V1092" "V1093" "V1094" "V1095" "V1096" "V1097" "V1098"
## [1099] "V1099" "V1100" "V1101" "V1102" "V1103" "V1104" "V1105" "V1106" "V1107"
## [1108] "V1108" "V1109" "V1110" "V1111" "V1112" "V1113" "V1114" "V1115" "V1116"
## [1117] "V1117" "V1118" "V1119" "V1120" "V1121" "V1122" "V1123" "V1124" "V1125"
## [1126] "V1126" "V1127" "V1128" "V1129" "V1130" "V1131" "V1132" "V1133" "V1134"
## [1135] "V1135" "V1136" "V1137" "V1138" "V1139" "V1140" "V1141" "V1142" "V1143"
## [1144] "V1144" "V1145" "V1146" "V1147" "V1148" "V1149" "V1150" "V1151" "V1152"
## [1153] "V1153" "V1154" "V1155" "V1156" "V1157" "V1158" "V1159" "V1160" "V1161"
## [1162] "V1162" "V1163" "V1164" "V1165" "V1166" "V1167" "V1168" "V1169" "V1170"
## [1171] "V1171" "V1172" "V1173" "V1174" "V1175" "V1176" "V1177" "V1178" "V1179"
## [1180] "V1180" "V1181" "V1182" "V1183" "V1184" "V1185" "V1186" "V1187" "V1188"
## [1189] "V1189" "V1190" "V1191" "V1192" "V1193" "V1194" "V1195" "V1196" "V1197"
## [1198] "V1198" "V1199" "V1200" "V1201" "V1202" "V1203" "V1204" "V1205" "V1206"
## [1207] "V1207" "V1208" "V1209" "V1210" "V1211" "V1212" "V1213" "V1214" "V1215"
## [1216] "V1216" "V1217" "V1218" "V1219" "V1220" "V1221" "V1222" "V1223" "V1224"
## [1225] "V1225" "V1226" "V1227" "V1228" "V1229" "V1230" "V1231" "V1232" "V1233"
## [1234] "V1234" "V1235" "V1236" "V1237" "V1238" "V1239" "V1240" "V1241" "V1242"
## [1243] "V1243" "V1244" "V1245" "V1246" "V1247" "V1248" "V1249" "V1250" "V1251"
## [1252] "V1252" "V1253" "V1254" "V1255" "V1256" "V1257" "V1258" "V1259" "V1260"
## [1261] "V1261" "V1262" "V1263" "V1264" "V1265" "V1266" "V1267" "V1268" "V1269"
## [1270] "V1270" "V1271" "V1272" "V1273" "V1274" "V1275" "V1276" "V1277" "V1278"
## [1279] "V1279" "V1280" "V1281" "V1282" "V1283" "V1284" "V1285" "V1286" "V1287"
## [1288] "V1288" "V1289" "V1290" "V1291" "V1292" "V1293" "V1294" "V1295" "V1296"
## [1297] "V1297" "V1298" "V1299" "V1300" "V1301" "V1302" "V1303" "V1304" "V1305"
## [1306] "V1306" "V1307" "V1308" "V1309" "V1310" "V1311" "V1312" "V1313" "V1314"
## [1315] "V1315" "V1316" "V1317" "V1318" "V1319" "V1320" "V1321" "V1322" "V1323"
## [1324] "V1324" "V1325" "V1326" "V1327" "V1328" "V1329" "V1330" "V1331" "V1332"
## [1333] "V1333" "V1334" "V1335" "V1336" "V1337" "V1338" "V1339" "V1340" "V1341"
## [1342] "V1342" "V1343" "V1344" "V1345" "V1346" "V1347" "V1348" "V1349" "V1350"
## [1351] "V1351" "V1352" "V1353" "V1354" "V1355" "V1356" "V1357" "V1358" "V1359"
## [1360] "V1360" "V1361" "V1362" "V1363" "V1364" "V1365" "V1366" "V1367" "V1368"
## [1369] "V1369" "V1370" "V1371" "V1372" "V1373" "V1374" "V1375" "V1376" "V1377"
## [1378] "V1378" "V1379" "V1380" "V1381" "V1382" "V1383" "V1384" "V1385" "V1386"
## [1387] "V1387" "V1388" "V1389" "V1390" "V1391" "V1392" "V1393" "V1394" "V1395"
## [1396] "V1396" "V1397" "V1398" "V1399" "V1400" "V1401" "V1402" "V1403" "V1404"
## [1405] "V1405" "V1406" "V1407" "V1408" "V1409" "V1410" "V1411" "V1412" "V1413"
## [1414] "V1414" "V1415" "V1416" "V1417" "V1418" "V1419" "V1420" "V1421" "V1422"
## [1423] "V1423" "V1424" "V1425" "V1426" "V1427" "V1428" "V1429" "V1430" "V1431"
## [1432] "V1432" "V1433" "V1434" "V1435" "V1436" "V1437" "V1438" "V1439" "V1440"
## [1441] "V1441" "V1442" "V1443" "V1444" "V1445" "V1446" "V1447" "V1448" "V1449"
## [1450] "V1450" "V1451" "V1452" "V1453" "V1454" "V1455" "V1456" "V1457" "V1458"
## [1459] "V1459" "V1460" "V1461" "V1462" "V1463" "V1464" "V1465" "V1466" "V1467"
## [1468] "V1468" "V1469" "V1470" "V1471" "V1472" "V1473" "V1474" "V1475" "V1476"
## [1477] "V1477" "V1478" "V1479" "V1480" "V1481" "V1482" "V1483" "V1484" "V1485"
## [1486] "V1486" "V1487" "V1488" "V1489" "V1490" "V1491" "V1492" "V1493" "V1494"
## [1495] "V1495" "V1496" "V1497" "V1498" "V1499" "V1500" "V1501" "V1502" "V1503"
## [1504] "V1504" "V1505" "V1506" "V1507" "V1508" "V1509" "V1510" "V1511" "V1512"
## [1513] "V1513" "V1514" "V1515" "V1516" "V1517" "V1518" "V1519" "V1520" "V1521"
## [1522] "V1522" "V1523" "V1524" "V1525" "V1526" "V1527" "V1528" "V1529" "V1530"
## [1531] "V1531" "V1532" "V1533" "V1534" "V1535" "V1536" "V1537" "V1538" "V1539"
## [1540] "V1540" "V1541" "V1542" "V1543" "V1544" "V1545" "V1546" "V1547" "V1548"
## [1549] "V1549" "V1550" "V1551" "V1552" "V1553" "V1554" "V1555" "V1556" "V1557"
## [1558] "V1558" "V1559" "V1560" "V1561" "V1562" "V1563" "V1564" "V1565" "V1566"
## [1567] "V1567" "V1568" "V1569" "V1570" "V1571" "V1572" "V1573" "V1574" "V1575"
## [1576] "V1576" "V1577" "V1578" "V1579" "V1580" "V1581" "V1582" "V1583" "V1584"
## [1585] "V1585" "V1586" "V1587" "V1588" "V1589" "V1590" "V1591" "V1592" "V1593"
## [1594] "V1594" "V1595" "V1596" "V1597" "V1598" "V1599" "V1600" "V1601" "V1602"
## [1603] "V1603" "V1604" "V1605" "V1606" "V1607" "V1608" "V1609" "V1610" "V1611"
## [1612] "V1612" "V1613" "V1614" "V1615" "V1616" "V1617" "V1618" "V1619" "V1620"
## [1621] "V1621" "V1622" "V1623" "V1624" "V1625" "V1626" "V1627" "V1628" "V1629"
## [1630] "V1630" "V1631" "V1632" "V1633" "V1634" "V1635" "V1636" "V1637" "V1638"
## [1639] "V1639" "V1640" "V1641" "V1642" "V1643" "V1644" "V1645" "V1646" "V1647"
## [1648] "V1648" "V1649" "V1650" "V1651" "V1652" "V1653" "V1654" "V1655" "V1656"
## [1657] "V1657" "V1658" "V1659" "V1660" "V1661" "V1662" "V1663" "V1664" "V1665"
## [1666] "V1666" "V1667" "V1668" "V1669" "V1670" "V1671" "V1672" "V1673" "V1674"
## [1675] "V1675" "V1676" "V1677" "V1678" "V1679" "V1680" "V1681" "V1682" "V1683"
## [1684] "V1684" "V1685" "V1686" "V1687" "V1688" "V1689" "V1690" "V1691" "V1692"
## [1693] "V1693" "V1694" "V1695" "V1696" "V1697" "V1698" "V1699" "V1700" "V1701"
## [1702] "V1702" "V1703" "V1704" "V1705" "V1706" "V1707" "V1708" "V1709" "V1710"
## [1711] "V1711" "V1712" "V1713" "V1714" "V1715" "V1716" "V1717" "V1718" "V1719"
## [1720] "V1720" "V1721" "V1722" "V1723" "V1724" "V1725" "V1726" "V1727" "V1728"
## [1729] "V1729" "V1730" "V1731" "V1732" "V1733" "V1734" "V1735" "V1736" "V1737"
## [1738] "V1738" "V1739" "V1740" "V1741" "V1742" "V1743" "V1744" "V1745" "V1746"
## [1747] "V1747" "V1748" "V1749" "V1750" "V1751" "V1752" "V1753" "V1754" "V1755"
## [1756] "V1756" "V1757" "V1758" "V1759" "V1760" "V1761" "V1762" "V1763" "V1764"
## [1765] "V1765" "V1766" "V1767" "V1768" "V1769" "V1770" "V1771" "V1772" "V1773"
## [1774] "V1774" "V1775" "V1776" "V1777" "V1778" "V1779" "V1780" "V1781" "V1782"
## [1783] "V1783" "V1784" "V1785" "V1786" "V1787" "V1788" "V1789" "V1790" "V1791"
## [1792] "V1792" "V1793" "V1794" "V1795" "V1796" "V1797" "V1798" "V1799" "V1800"
## [1801] "V1801" "V1802" "V1803" "V1804" "V1805" "V1806" "V1807" "V1808" "V1809"
## [1810] "V1810" "V1811" "V1812" "V1813" "V1814" "V1815" "V1816" "V1817" "V1818"
## [1819] "V1819" "V1820" "V1821" "V1822" "V1823" "V1824" "V1825" "V1826" "V1827"
## [1828] "V1828" "V1829" "V1830" "V1831" "V1832" "V1833" "V1834" "V1835" "V1836"
## [1837] "V1837" "V1838" "V1839" "V1840" "V1841" "V1842" "V1843" "V1844" "V1845"
## [1846] "V1846" "V1847" "V1848" "V1849" "V1850" "V1851" "V1852" "V1853" "V1854"
## [1855] "V1855" "V1856" "V1857" "V1858" "V1859" "V1860" "V1861" "V1862" "V1863"
## [1864] "V1864" "V1865" "V1866" "V1867" "V1868" "V1869" "V1870" "V1871" "V1872"
## [1873] "V1873" "V1874" "V1875" "V1876" "V1877" "V1878" "V1879" "V1880" "V1881"
## [1882] "V1882" "V1883" "V1884" "V1885" "V1886" "V1887" "V1888" "V1889" "V1890"
## [1891] "V1891" "V1892" "V1893" "V1894" "V1895" "V1896" "V1897" "V1898" "V1899"
## [1900] "V1900" "V1901" "V1902" "V1903" "V1904" "V1905" "V1906" "V1907" "V1908"
## [1909] "V1909" "V1910" "V1911" "V1912" "V1913" "V1914" "V1915" "V1916" "V1917"
## [1918] "V1918" "V1919" "V1920" "V1921" "V1922" "V1923" "V1924" "V1925" "V1926"
## [1927] "V1927" "V1928" "V1929" "V1930" "V1931" "V1932" "V1933" "V1934" "V1935"
## [1936] "V1936" "V1937" "V1938" "V1939" "V1940" "V1941" "V1942" "V1943" "V1944"
## [1945] "V1945" "V1946" "V1947" "V1948" "V1949" "V1950" "V1951" "V1952" "V1953"
## [1954] "V1954" "V1955" "V1956" "V1957" "V1958" "V1959" "V1960" "V1961" "V1962"
## [1963] "V1963" "V1964" "V1965" "V1966" "V1967" "V1968" "V1969" "V1970" "V1971"
## [1972] "V1972" "V1973" "V1974" "V1975" "V1976" "V1977" "V1978" "V1979" "V1980"
## [1981] "V1981" "V1982" "V1983" "V1984" "V1985" "V1986" "V1987" "V1988" "V1989"
## [1990] "V1990" "V1991" "V1992" "V1993" "V1994" "V1995" "V1996" "V1997" "V1998"
## [1999] "V1999" "V2000" "V2001" "V2002" "V2003" "V2004" "V2005" "V2006" "V2007"
## [2008] "V2008" "V2009" "V2010" "V2011" "V2012" "V2013" "V2014" "V2015" "V2016"
## [2017] "V2017" "V2018" "V2019" "V2020" "V2021" "V2022" "V2023" "V2024" "V2025"
## [2026] "V2026" "V2027" "V2028" "V2029" "V2030" "V2031" "V2032" "V2033" "V2034"
## [2035] "V2035" "V2036" "V2037" "V2038" "V2039" "V2040" "V2041" "V2042" "V2043"
## [2044] "V2044" "V2045" "V2046" "V2047" "V2048" "V2049" "V2050" "V2051" "V2052"
## [2053] "V2053" "V2054" "V2055" "V2056" "V2057" "V2058" "V2059" "V2060" "V2061"
## [2062] "V2062" "V2063" "V2064" "V2065" "V2066" "V2067" "V2068" "V2069" "V2070"
## [2071] "V2071" "V2072" "V2073" "V2074" "V2075" "V2076" "V2077" "V2078" "V2079"
## [2080] "V2080" "V2081" "V2082" "V2083" "V2084" "V2085" "V2086" "V2087" "V2088"
## [2089] "V2089" "V2090" "V2091" "V2092" "V2093" "V2094" "V2095" "V2096" "V2097"
## [2098] "V2098" "V2099" "V2100" "V2101" "V2102" "V2103" "V2104" "V2105" "V2106"
## [2107] "V2107" "V2108" "V2109" "V2110" "V2111" "V2112" "V2113" "V2114" "V2115"
## [2116] "V2116" "V2117" "V2118" "V2119" "V2120" "V2121" "V2122" "V2123" "V2124"
## [2125] "V2125" "V2126" "V2127" "V2128" "V2129" "V2130" "V2131" "V2132" "V2133"
## [2134] "V2134" "V2135" "V2136" "V2137" "V2138" "V2139" "V2140" "V2141" "V2142"
## [2143] "V2143" "V2144" "V2145" "V2146" "V2147" "V2148" "V2149" "V2150" "V2151"
## [2152] "V2152" "V2153" "V2154" "V2155" "V2156" "V2157" "V2158" "V2159" "V2160"
## [2161] "V2161" "V2162" "V2163" "V2164" "V2165" "V2166" "V2167" "V2168" "V2169"
## [2170] "V2170" "V2171" "V2172" "V2173" "V2174" "V2175" "V2176" "V2177" "V2178"
## [2179] "V2179" "V2180" "V2181" "V2182" "V2183" "V2184" "V2185" "V2186" "V2187"
## [2188] "V2188" "V2189" "V2190" "V2191" "V2192" "V2193" "V2194" "V2195" "V2196"
## [2197] "V2197" "V2198" "V2199" "V2200" "V2201" "V2202" "V2203" "V2204" "V2205"
## [2206] "V2206" "V2207" "V2208" "V2209" "V2210" "V2211" "V2212" "V2213" "V2214"
## [2215] "V2215" "V2216" "V2217" "V2218" "V2219" "V2220" "V2221" "V2222" "V2223"
## [2224] "V2224" "V2225" "V2226" "V2227" "V2228" "V2229" "V2230" "V2231" "V2232"
## [2233] "V2233" "V2234" "V2235" "V2236" "V2237" "V2238" "V2239" "V2240" "V2241"
## [2242] "V2242" "V2243" "V2244" "V2245" "V2246" "V2247" "V2248" "V2249" "V2250"
## [2251] "V2251" "V2252" "V2253" "V2254" "V2255" "V2256" "V2257" "V2258" "V2259"
## [2260] "V2260" "V2261" "V2262" "V2263" "V2264" "V2265" "V2266" "V2267" "V2268"
## [2269] "V2269" "V2270" "V2271" "V2272" "V2273" "V2274" "V2275" "V2276" "V2277"
## [2278] "V2278" "V2279" "V2280" "V2281" "V2282" "V2283" "V2284" "V2285" "V2286"
## [2287] "V2287" "V2288" "V2289" "V2290" "V2291" "V2292" "V2293" "V2294" "V2295"
## [2296] "V2296" "V2297" "V2298" "V2299" "V2300" "V2301" "V2302" "V2303" "V2304"
## [2305] "V2305" "V2306" "V2307" "V2308" "V2309" "V2310" "V2311" "V2312" "V2313"
## [2314] "V2314" "V2315" "V2316" "V2317" "V2318" "V2319" "V2320" "V2321" "V2322"
## [2323] "V2323" "V2324" "V2325" "V2326" "V2327" "V2328" "V2329" "V2330" "V2331"
## [2332] "V2332" "V2333" "V2334" "V2335" "V2336" "V2337" "V2338" "V2339" "V2340"
## [2341] "V2341" "V2342" "V2343" "V2344" "V2345" "V2346" "V2347" "V2348" "V2349"
## [2350] "V2350" "V2351" "V2352" "V2353" "V2354" "V2355" "V2356" "V2357" "V2358"
## [2359] "V2359" "V2360" "V2361" "V2362" "V2363" "V2364" "V2365" "V2366" "V2367"
## [2368] "V2368" "V2369" "V2370" "V2371" "V2372" "V2373" "V2374" "V2375" "V2376"
## [2377] "V2377" "V2378" "V2379" "V2380" "V2381" "V2382" "V2383" "V2384" "V2385"
## [2386] "V2386" "V2387" "V2388" "V2389" "V2390" "V2391" "V2392" "V2393" "V2394"
## [2395] "V2395" "V2396" "V2397" "V2398" "V2399" "V2400" "V2401" "V2402" "V2403"
## [2404] "V2404" "V2405" "V2406" "V2407" "V2408" "V2409" "V2410" "V2411" "V2412"
## [2413] "V2413" "V2414" "V2415" "V2416" "V2417" "V2418" "V2419" "V2420" "V2421"
## [2422] "V2422" "V2423" "V2424" "V2425" "V2426" "V2427" "V2428" "V2429" "V2430"
## [2431] "V2431" "V2432" "V2433" "V2434" "V2435" "V2436" "V2437" "V2438" "V2439"
## [2440] "V2440" "V2441" "V2442" "V2443" "V2444" "V2445" "V2446" "V2447" "V2448"
## [2449] "V2449" "V2450" "V2451" "V2452" "V2453" "V2454" "V2455" "V2456" "V2457"
## [2458] "V2458" "V2459" "V2460" "V2461" "V2462" "V2463" "V2464" "V2465" "V2466"
## [2467] "V2467" "V2468" "V2469" "V2470" "V2471" "V2472" "V2473" "V2474" "V2475"
## [2476] "V2476" "V2477" "V2478" "V2479" "V2480" "V2481" "V2482" "V2483" "V2484"
## [2485] "V2485" "V2486" "V2487" "V2488" "V2489" "V2490" "V2491" "V2492" "V2493"
## [2494] "V2494" "V2495" "V2496" "V2497" "V2498" "V2499" "V2500" "V2501" "V2502"
## [2503] "V2503" "V2504" "V2505" "V2506" "V2507" "V2508" "V2509" "V2510" "V2511"
## [2512] "V2512" "V2513" "V2514" "V2515" "V2516" "V2517" "V2518" "V2519" "V2520"
## [2521] "V2521" "V2522" "V2523" "V2524" "V2525" "V2526" "V2527" "V2528" "V2529"
## [2530] "V2530" "V2531" "V2532" "V2533" "V2534" "V2535" "V2536" "V2537" "V2538"
## [2539] "V2539" "V2540" "V2541" "V2542" "V2543" "V2544" "V2545" "V2546" "V2547"
## [2548] "V2548" "V2549" "V2550" "V2551" "V2552" "V2553" "V2554" "V2555" "V2556"
## [2557] "V2557" "V2558" "V2559" "V2560" "V2561" "V2562" "V2563" "V2564" "V2565"
## [2566] "V2566" "V2567" "V2568" "V2569" "V2570" "V2571" "V2572" "V2573" "V2574"
## [2575] "V2575" "V2576" "V2577" "V2578" "V2579" "V2580" "V2581" "V2582" "V2583"
## [2584] "V2584" "V2585" "V2586" "V2587" "V2588" "V2589" "V2590" "V2591" "V2592"
## [2593] "V2593" "V2594" "V2595" "V2596" "V2597" "V2598" "V2599" "V2600" "V2601"
## [2602] "V2602" "V2603" "V2604" "V2605" "V2606" "V2607" "V2608" "V2609" "V2610"
## [2611] "V2611" "V2612" "V2613" "V2614" "V2615" "V2616" "V2617" "V2618" "V2619"
## [2620] "V2620" "V2621" "V2622" "V2623" "V2624" "V2625" "V2626" "V2627" "V2628"
## [2629] "V2629" "V2630" "V2631" "V2632" "V2633" "V2634" "V2635" "V2636" "V2637"
## [2638] "V2638" "V2639" "V2640" "V2641" "V2642" "V2643" "V2644" "V2645" "V2646"
## [2647] "V2647" "V2648" "V2649" "V2650" "V2651" "V2652" "V2653" "V2654" "V2655"
## [2656] "V2656" "V2657" "V2658" "V2659" "V2660" "V2661" "V2662" "V2663" "V2664"
## [2665] "V2665" "V2666" "V2667" "V2668" "V2669" "V2670" "V2671" "V2672" "V2673"
## [2674] "V2674" "V2675" "V2676" "V2677" "V2678" "V2679" "V2680" "V2681" "V2682"
## [2683] "V2683" "V2684" "V2685" "V2686" "V2687" "V2688" "V2689" "V2690" "V2691"
## [2692] "V2692" "V2693" "V2694" "V2695" "V2696" "V2697" "V2698" "V2699" "V2700"
## [2701] "V2701" "V2702" "V2703" "V2704" "V2705" "V2706" "V2707" "V2708" "V2709"
## [2710] "V2710" "V2711" "V2712" "V2713" "V2714" "V2715" "V2716" "V2717" "V2718"
## [2719] "V2719" "V2720" "V2721" "V2722" "V2723" "V2724" "V2725" "V2726" "V2727"
## [2728] "V2728" "V2729" "V2730" "V2731" "V2732" "V2733" "V2734" "V2735" "V2736"
## [2737] "V2737" "V2738" "V2739" "V2740" "V2741" "V2742" "V2743" "V2744" "V2745"
## [2746] "V2746" "V2747" "V2748" "V2749" "V2750" "V2751" "V2752" "V2753" "V2754"
## [2755] "V2755" "V2756" "V2757" "V2758" "V2759" "V2760" "V2761" "V2762" "V2763"
## [2764] "V2764" "V2765" "V2766" "V2767" "V2768" "V2769" "V2770" "V2771" "V2772"
## [2773] "V2773" "V2774" "V2775" "V2776" "V2777" "V2778" "V2779" "V2780" "V2781"
## [2782] "V2782" "V2783" "V2784" "V2785" "V2786" "V2787" "V2788" "V2789" "V2790"
## [2791] "V2791" "V2792" "V2793" "V2794" "V2795" "V2796" "V2797" "V2798" "V2799"
## [2800] "V2800" "V2801" "V2802" "V2803" "V2804" "V2805" "V2806" "V2807" "V2808"
## [2809] "V2809" "V2810" "V2811" "V2812" "V2813" "V2814" "V2815" "V2816" "V2817"
## [2818] "V2818" "V2819" "V2820" "V2821" "V2822" "V2823" "V2824" "V2825" "V2826"
## [2827] "V2827" "V2828" "V2829" "V2830" "V2831" "V2832" "V2833" "V2834" "V2835"
## [2836] "V2836" "V2837" "V2838" "V2839" "V2840" "V2841" "V2842" "V2843" "V2844"
## [2845] "V2845" "V2846" "V2847" "V2848" "V2849" "V2850" "V2851" "V2852" "V2853"
## [2854] "V2854" "V2855" "V2856" "V2857" "V2858" "V2859" "V2860" "V2861" "V2862"
## [2863] "V2863" "V2864" "V2865" "V2866" "V2867" "V2868" "V2869" "V2870" "V2871"
## [2872] "V2872" "V2873" "V2874" "V2875" "V2876" "V2877" "V2878" "V2879" "V2880"
## [2881] "V2881" "V2882" "V2883" "V2884" "V2885" "V2886" "V2887" "V2888" "V2889"
## [2890] "V2890" "V2891" "V2892" "V2893" "V2894" "V2895" "V2896" "V2897" "V2898"
## [2899] "V2899" "V2900" "V2901" "V2902" "V2903" "V2904" "V2905" "V2906" "V2907"
## [2908] "V2908" "V2909" "V2910" "V2911" "V2912" "V2913" "V2914" "V2915" "V2916"
## [2917] "V2917" "V2918" "V2919" "V2920" "V2921" "V2922" "V2923" "V2924" "V2925"
## [2926] "V2926" "V2927" "V2928" "V2929" "V2930" "V2931" "V2932" "V2933" "V2934"
## [2935] "V2935" "V2936" "V2937" "V2938" "V2939" "V2940" "V2941" "V2942" "V2943"
## [2944] "V2944" "V2945" "V2946" "V2947" "V2948" "V2949" "V2950" "V2951" "V2952"
## [2953] "V2953" "V2954" "V2955" "V2956" "V2957" "V2958" "V2959" "V2960" "V2961"
## [2962] "V2962" "V2963" "V2964" "V2965" "V2966" "V2967" "V2968" "V2969" "V2970"
## [2971] "V2971" "V2972" "V2973" "V2974" "V2975" "V2976" "V2977" "V2978" "V2979"
## [2980] "V2980" "V2981" "V2982" "V2983" "V2984" "V2985" "V2986" "V2987" "V2988"
## [2989] "V2989" "V2990" "V2991" "V2992" "V2993" "V2994" "V2995" "V2996" "V2997"
## [2998] "V2998" "V2999" "V3000" "V3001" "V3002" "V3003" "V3004" "V3005" "V3006"
## [3007] "V3007" "V3008" "V3009" "V3010" "V3011" "V3012" "V3013" "V3014" "V3015"
## [3016] "V3016" "V3017" "V3018" "V3019" "V3020" "V3021" "V3022" "V3023" "V3024"
## [3025] "V3025" "V3026" "V3027" "V3028" "V3029" "V3030" "V3031" "V3032" "V3033"
## [3034] "V3034" "V3035" "V3036" "V3037" "V3038" "V3039" "V3040" "V3041" "V3042"
## [3043] "V3043" "V3044" "V3045" "V3046" "V3047" "V3048" "V3049" "V3050" "V3051"
## [3052] "V3052" "V3053" "V3054" "V3055" "V3056" "V3057" "V3058" "V3059" "V3060"
## [3061] "V3061" "V3062" "V3063" "V3064" "V3065" "V3066" "V3067" "V3068" "V3069"
## [3070] "V3070" "V3071" "V3072" "V3073" "V3074" "V3075" "V3076" "V3077" "V3078"
## [3079] "V3079" "V3080" "V3081" "V3082" "V3083" "V3084" "V3085" "V3086" "V3087"
## [3088] "V3088" "V3089" "V3090" "V3091" "V3092" "V3093" "V3094" "V3095" "V3096"
## [3097] "V3097" "V3098" "V3099" "V3100" "V3101" "V3102" "V3103" "V3104" "V3105"
## [3106] "V3106" "V3107" "V3108" "V3109" "V3110" "V3111" "V3112" "V3113" "V3114"
## [3115] "V3115" "V3116" "V3117" "V3118" "V3119" "V3120" "V3121" "V3122" "V3123"
## [3124] "V3124" "V3125" "V3126" "V3127" "V3128" "V3129" "V3130" "V3131" "V3132"
## [3133] "V3133" "V3134" "V3135" "V3136" "V3137" "V3138" "V3139" "V3140" "V3141"
## [3142] "V3142" "V3143" "V3144" "V3145" "V3146" "V3147" "V3148" "V3149" "V3150"
## [3151] "V3151" "V3152" "V3153" "V3154" "V3155" "V3156" "V3157" "V3158" "V3159"
## [3160] "V3160" "V3161" "V3162" "V3163" "V3164" "V3165" "V3166" "V3167" "V3168"
## [3169] "V3169" "V3170" "V3171" "V3172" "V3173" "V3174" "V3175" "V3176" "V3177"
## [3178] "V3178" "V3179" "V3180" "V3181" "V3182" "V3183" "V3184" "V3185" "V3186"
## [3187] "V3187" "V3188" "V3189" "V3190" "V3191" "V3192" "V3193" "V3194" "V3195"
## [3196] "V3196" "V3197" "V3198" "V3199" "V3200" "V3201" "V3202" "V3203" "V3204"
## [3205] "V3205" "V3206" "V3207" "V3208" "V3209" "V3210" "V3211" "V3212" "V3213"
## [3214] "V3214" "V3215" "V3216" "V3217" "V3218" "V3219" "V3220" "V3221" "V3222"
## [3223] "V3223" "V3224" "V3225" "V3226" "V3227" "V3228" "V3229" "V3230" "V3231"
## [3232] "V3232" "V3233" "V3234" "V3235" "V3236" "V3237" "V3238" "V3239" "V3240"
## [3241] "V3241" "V3242" "V3243" "V3244" "V3245" "V3246" "V3247" "V3248" "V3249"
## [3250] "V3250" "V3251" "V3252" "V3253" "V3254" "V3255" "V3256" "V3257" "V3258"
## [3259] "V3259" "V3260" "V3261" "V3262" "V3263" "V3264" "V3265" "V3266" "V3267"
## [3268] "V3268" "V3269" "V3270" "V3271" "V3272" "V3273" "V3274" "V3275" "V3276"
## [3277] "V3277" "V3278" "V3279" "V3280" "V3281" "V3282" "V3283" "V3284" "V3285"
## [3286] "V3286" "V3287" "V3288" "V3289" "V3290" "V3291" "V3292" "V3293" "V3294"
## [3295] "V3295" "V3296" "V3297" "V3298" "V3299" "V3300" "V3301" "V3302" "V3303"
## [3304] "V3304" "V3305" "V3306" "V3307" "V3308" "V3309" "V3310" "V3311" "V3312"
## [3313] "V3313" "V3314" "V3315" "V3316" "V3317" "V3318" "V3319" "V3320" "V3321"
## [3322] "V3322" "V3323" "V3324" "V3325" "V3326" "V3327" "V3328" "V3329" "V3330"
## [3331] "V3331" "V3332" "V3333" "V3334" "V3335" "V3336" "V3337" "V3338" "V3339"
## [3340] "V3340" "V3341" "V3342" "V3343" "V3344" "V3345" "V3346" "V3347" "V3348"
## [3349] "V3349" "V3350" "V3351" "V3352" "V3353" "V3354" "V3355" "V3356" "V3357"
## [3358] "V3358" "V3359" "V3360" "V3361" "V3362" "V3363" "V3364" "V3365" "V3366"
## [3367] "V3367" "V3368" "V3369" "V3370" "V3371" "V3372" "V3373" "V3374" "V3375"
## [3376] "V3376" "V3377" "V3378" "V3379" "V3380" "V3381" "V3382" "V3383" "V3384"
## [3385] "V3385" "V3386" "V3387" "V3388" "V3389" "V3390" "V3391" "V3392" "V3393"
## [3394] "V3394" "V3395" "V3396" "V3397" "V3398" "V3399" "V3400" "V3401" "V3402"
## [3403] "V3403" "V3404" "V3405" "V3406" "V3407" "V3408" "V3409" "V3410" "V3411"
## [3412] "V3412" "V3413" "V3414" "V3415" "V3416" "V3417" "V3418" "V3419" "V3420"
## [3421] "V3421" "V3422" "V3423" "V3424" "V3425" "V3426" "V3427" "V3428" "V3429"
## [3430] "V3430" "V3431" "V3432" "V3433" "V3434" "V3435" "V3436" "V3437" "V3438"
## [3439] "V3439" "V3440" "V3441" "V3442" "V3443" "V3444" "V3445" "V3446" "V3447"
## [3448] "V3448" "V3449" "V3450" "V3451" "V3452" "V3453" "V3454" "V3455" "V3456"
## [3457] "V3457" "V3458" "V3459" "V3460" "V3461" "V3462" "V3463" "V3464" "V3465"
## [3466] "V3466" "V3467" "V3468" "V3469" "V3470" "V3471" "V3472" "V3473" "V3474"
## [3475] "V3475" "V3476" "V3477" "V3478" "V3479" "V3480" "V3481" "V3482" "V3483"
## [3484] "V3484" "V3485" "V3486" "V3487" "V3488" "V3489" "V3490" "V3491" "V3492"
## [3493] "V3493" "V3494" "V3495" "V3496" "V3497" "V3498" "V3499" "V3500" "V3501"
## [3502] "V3502" "V3503" "V3504" "V3505" "V3506" "V3507" "V3508" "V3509" "V3510"
## [3511] "V3511" "V3512" "V3513" "V3514" "V3515" "V3516" "V3517" "V3518" "V3519"
## [3520] "V3520" "V3521" "V3522" "V3523" "V3524" "V3525" "V3526" "V3527" "V3528"
## [3529] "V3529" "V3530" "V3531" "V3532" "V3533" "V3534" "V3535" "V3536" "V3537"
## [3538] "V3538" "V3539" "V3540" "V3541" "V3542" "V3543" "V3544" "V3545" "V3546"
## [3547] "V3547" "V3548" "V3549" "V3550" "V3551" "V3552" "V3553" "V3554" "V3555"
## [3556] "V3556" "V3557" "V3558" "V3559" "V3560" "V3561" "V3562" "V3563" "V3564"
## [3565] "V3565" "V3566" "V3567" "V3568" "V3569" "V3570" "V3571" "V3572" "V3573"
## [3574] "V3574" "V3575" "V3576" "V3577" "V3578" "V3579" "V3580" "V3581" "V3582"
## [3583] "V3583" "V3584" "V3585" "V3586" "V3587" "V3588" "V3589" "V3590" "V3591"
## [3592] "V3592" "V3593" "V3594" "V3595" "V3596" "V3597" "V3598" "V3599" "V3600"
## [3601] "V3601" "V3602" "V3603" "V3604" "V3605" "V3606" "V3607" "V3608" "V3609"
## [3610] "V3610" "V3611" "V3612" "V3613" "V3614" "V3615" "V3616" "V3617" "V3618"
## [3619] "V3619" "V3620" "V3621" "V3622" "V3623" "V3624" "V3625" "V3626" "V3627"
## [3628] "V3628" "V3629" "V3630" "V3631" "V3632" "V3633" "V3634" "V3635" "V3636"
## [3637] "V3637" "V3638" "V3639" "V3640" "V3641" "V3642" "V3643" "V3644" "V3645"
## [3646] "V3646" "V3647" "V3648" "V3649" "V3650" "V3651" "V3652" "V3653" "V3654"
## [3655] "V3655" "V3656" "V3657" "V3658" "V3659" "V3660" "V3661" "V3662" "V3663"
## [3664] "V3664" "V3665" "V3666" "V3667" "V3668" "V3669" "V3670" "V3671" "V3672"
## [3673] "V3673" "V3674" "V3675" "V3676" "V3677" "V3678" "V3679" "V3680" "V3681"
## [3682] "V3682" "V3683" "V3684" "V3685" "V3686" "V3687" "V3688" "V3689" "V3690"
## [3691] "V3691" "V3692" "V3693" "V3694" "V3695" "V3696" "V3697" "V3698" "V3699"
## [3700] "V3700" "V3701" "V3702" "V3703" "V3704" "V3705" "V3706" "V3707" "V3708"
## [3709] "V3709" "V3710" "V3711" "V3712" "V3713" "V3714" "V3715" "V3716" "V3717"
## [3718] "V3718" "V3719" "V3720" "V3721" "V3722" "V3723" "V3724" "V3725" "V3726"
## [3727] "V3727" "V3728" "V3729" "V3730" "V3731" "V3732" "V3733" "V3734" "V3735"
## [3736] "V3736" "V3737" "V3738" "V3739" "V3740" "V3741" "V3742" "V3743" "V3744"
## [3745] "V3745" "V3746" "V3747" "V3748" "V3749" "V3750" "V3751" "V3752" "V3753"
## [3754] "V3754" "V3755" "V3756" "V3757" "V3758" "V3759" "V3760" "V3761" "V3762"
## [3763] "V3763" "V3764" "V3765" "V3766" "V3767" "V3768" "V3769" "V3770" "V3771"
## [3772] "V3772" "V3773" "V3774" "V3775" "V3776" "V3777" "V3778" "V3779" "V3780"
## [3781] "V3781" "V3782" "V3783" "V3784" "V3785" "V3786" "V3787" "V3788" "V3789"
## [3790] "V3790" "V3791" "V3792" "V3793" "V3794" "V3795" "V3796" "V3797" "V3798"
## [3799] "V3799" "V3800" "V3801" "V3802" "V3803" "V3804" "V3805" "V3806" "V3807"
## [3808] "V3808" "V3809" "V3810" "V3811" "V3812" "V3813" "V3814" "V3815" "V3816"
## [3817] "V3817" "V3818" "V3819" "V3820" "V3821" "V3822" "V3823" "V3824" "V3825"
## [3826] "V3826" "V3827" "V3828" "V3829" "V3830" "V3831" "V3832" "V3833" "V3834"
## [3835] "V3835" "V3836" "V3837" "V3838" "V3839" "V3840" "V3841" "V3842" "V3843"
## [3844] "V3844" "V3845" "V3846" "V3847" "V3848" "V3849" "V3850" "V3851" "V3852"
## [3853] "V3853" "V3854" "V3855" "V3856" "V3857" "V3858" "V3859" "V3860" "V3861"
## [3862] "V3862" "V3863" "V3864" "V3865" "V3866" "V3867" "V3868" "V3869" "V3870"
## [3871] "V3871" "V3872" "V3873" "V3874" "V3875" "V3876" "V3877" "V3878" "V3879"
## [3880] "V3880" "V3881" "V3882" "V3883" "V3884" "V3885" "V3886" "V3887" "V3888"
## [3889] "V3889" "V3890" "V3891" "V3892" "V3893" "V3894" "V3895" "V3896" "V3897"
## [3898] "V3898" "V3899" "V3900" "V3901" "V3902" "V3903" "V3904" "V3905" "V3906"
## [3907] "V3907" "V3908" "V3909" "V3910" "V3911" "V3912" "V3913" "V3914" "V3915"
## [3916] "V3916" "V3917" "V3918" "V3919" "V3920" "V3921" "V3922" "V3923" "V3924"
## [3925] "V3925" "V3926" "V3927" "V3928" "V3929" "V3930" "V3931" "V3932" "V3933"
## [3934] "V3934" "V3935" "V3936" "V3937" "V3938" "V3939" "V3940" "V3941" "V3942"
## [3943] "V3943" "V3944" "V3945" "V3946" "V3947" "V3948" "V3949" "V3950" "V3951"
## [3952] "V3952" "V3953" "V3954" "V3955" "V3956" "V3957" "V3958" "V3959" "V3960"
## [3961] "V3961" "V3962" "V3963" "V3964" "V3965" "V3966" "V3967" "V3968" "V3969"
## [3970] "V3970" "V3971" "V3972" "V3973" "V3974" "V3975" "V3976" "V3977" "V3978"
## [3979] "V3979" "V3980" "V3981" "V3982" "V3983" "V3984" "V3985" "V3986" "V3987"
## [3988] "V3988" "V3989" "V3990" "V3991" "V3992" "V3993" "V3994" "V3995" "V3996"
## [3997] "V3997" "V3998" "V3999" "V4000"
##
## $class
## [1] "data.frame"
##
## $row.names
## [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
## [19] 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
## [37] 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54
## [55] 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72
## [73] 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90
## [91] 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108
## [109] 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126
## [127] 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144
## [145] 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162
## [163] 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180
## [181] 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198
## [199] 199 200# las filas son el número de puntos de evaluación de la función y las columnas el número de curvas
# Suavizamiento spline
# Creación de la base de funciones
npuntos <- nrow(imagenfragilxeydf)
base_bspline <- create.bspline.basis(c(1, npuntos), 150)
plot(base_bspline)
summary(base_bspline)##
## Basis object:
##
## Type: bspline
##
## Range: 1 to 200
##
## Number of basis functions: 150# Selección de lambda
gcv <- NULL
lambda_list <- seq(-2, 4, length.out = 30)
# estos son las potencias de 10 de variación del lambda
# inicia con valores muy cercanos a cero 10^-2 hasta 10^4
matrix_data <- as.matrix(imagenfragilxeydf)
for (lambda in lambda_list) {
lambda <- 10**lambda
param_lambda <- fdPar(base_bspline,
2,
lambda)
fd_smoothfragil <- smooth.basis(argvals = seq(1,
nrow(matrix_data)),
y = matrix_data,
fdParobj = param_lambda)
gcv <- c(gcv, sum(fd_smoothfragil$gcv))
}
# Se esta tomando como criterio total la suma de las VC de todas las curvas
plotgcv <-
data.frame(log_lambda = lambda_list,
gcv = gcv) %>% ggplot(aes(x = log_lambda, y = gcv)) +
geom_line(color = "purple", linetype = "dashed") +
theme_light() +
scale_x_continuous(limits = c(0, 4))
plotly::ggplotly(plotgcv)selected_lamdba <- 10**lambda_list[which.min(gcv)]
print(selected_lamdba)## [1] 0.02592944print(log(selected_lamdba, 10))## [1] -1.586207# entrega el valor de lambda donde se minimiza la suma de VC y log de lambda
# Suavizamiento con el lambda elegido
param_lambda <- fdPar(base_bspline,
2,
lambda = selected_lamdba)
fd_smoothfragil <- smooth.basis(argvals = seq(1,
nrow(matrix_data)),
y = matrix_data,
fdParobj = param_lambda)
plot(fd_smoothfragil, xlab= "Pixel", ylab = "Intensidad Totas Las Imagenes")
## [1] "done"# una curva por cada foto
# Comparación de curvas originales y suavizadas
fd_fittedfragil <- fitted(fd_smoothfragil)
plot(imagenfragilxey[,1],type = "o",xlab="Pixel",ylab="Intensidad Ent1")
lines(fd_fittedfragil[,1],col="2")
plot(imagenfragilxey[,401],type = "o",xlab="Pixel",ylab="Intensidad Ent2")
lines(fd_fittedfragil[,401],col="2")
plot(imagenfragilxey[,801],type = "o",xlab="Pixel",ylab="Intensidad Ent3")
lines(fd_fittedfragil[,801],col="2")
plot(imagenfragilxey[,1201],type = "o",xlab="Pixel",ylab="Intensidad Ent4")
lines(fd_fittedfragil[,1201],col="2")
plot(imagenfragilxey[,1601],type = "o",xlab="Pixel",ylab="Intensidad Ent5")
lines(fd_fittedfragil[,1601],col="2")
plot(imagenfragilxey[,2001],type = "o",xlab="Pixel",ylab="Intensidad Ent6")
lines(fd_fittedfragil[,2001],col="2")
plot(imagenfragilxey[,2401],type = "o",xlab="Pixel",ylab="Intensidad Ent7")
lines(fd_fittedfragil[,2401],col="2")
plot(imagenfragilxey[,2801],type = "o",xlab="Pixel",ylab="Intensidad Ens1")
lines(fd_fittedfragil[,2801],col="2")
plot(imagenfragilxey[,3201],type = "o",xlab="Pixel",ylab="Intensidad Ens2")
lines(fd_fittedfragil[,3201],col="2")
plot(imagenfragilxey[,3601],type = "o",xlab="Pixel",ylab="Intensidad Ens3")
lines(fd_fittedfragil[,3601],col="2")
2.1 Función de varianza imagen frágil
Para ello se usa la función var.fd. En este caso se divide el recorrido en 200 puntos (igual que los pixeles).
Se calcula el operador de los datos de entrenamiento como conjunto y el de cada imagen de ensayo por separado.
var_fdfragilEnt <- var.fd(fd_smoothfragil$fd[1:2800])
var_fdfragilEns1 <- var.fd(fd_smoothfragil$fd[2801:3200])
var_fdfragilEns2 <- var.fd(fd_smoothfragil$fd[3201:3600])
var_fdfragilEns3 <- var.fd(fd_smoothfragil$fd[3601:4000])
# Calcula la varianza del objeto funcional de cada imagen
# La salida es un objeto bivariado funcional
# Necesita dos bases una para cada eje
eva <- seq(1, npuntos, length = 200)
matriz_var_fragilEnt <- eval.bifd(eva, eva, var_fdfragilEnt)
matriz_var_fragilEns1 <- eval.bifd(eva, eva, var_fdfragilEns1)
matriz_var_fragilEns2 <- eval.bifd(eva, eva, var_fdfragilEns2)
matriz_var_fragilEns3 <- eval.bifd(eva, eva, var_fdfragilEns3)3. Cargar imagenes fatiga
Total de imagenes 10. Por cada foto 400 datos funcionales (lineas de pixeles en X y líneas de pixeles en y), para un total de 4000 datos.
imagenfatigaent1 <- read.bitmap("FatigaEnt1.jpg") # crea una matriz de x filas y columanas y z=3 canales
imagenfatigaent1 <- imagenfatigaent1 [,,1] # Deja un solo canal
imagenfatigaent1t <- t(imagenfatigaent1)
imagenfatigaent1xey <- rbind(imagenfatigaent1,imagenfatigaent1t)
imagenfatigaent1xey <- t(imagenfatigaent1xey)
dim(imagenfatigaent1xey)## [1] 200 400imagenfatigaent2 <- read.bitmap("FatigaEnt2.jpg") # crea una matriz de x filas y columanas y z=3 canales
imagenfatigaent2 <- imagenfatigaent2 [,,1] # Deja un solo canal
imagenfatigaent2t <- t(imagenfatigaent2)
imagenfatigaent2xey <- rbind(imagenfatigaent2,imagenfatigaent2t)
imagenfatigaent2xey <- t(imagenfatigaent2xey)
dim(imagenfatigaent2xey)## [1] 200 400imagenfatigaent3 <- read.bitmap("FatigaEnt3.jpg") # crea una matriz de x filas y columanas y z=3 canales
imagenfatigaent3 <- imagenfatigaent3 [,,1] # Deja un solo canal
imagenfatigaent3t <- t(imagenfatigaent3)
imagenfatigaent3xey <- rbind(imagenfatigaent3,imagenfatigaent3t)
imagenfatigaent3xey <- t(imagenfatigaent3xey)
dim(imagenfatigaent3xey)## [1] 200 400imagenfatigaent4 <- read.bitmap("FatigaEnt4.jpg") # crea una matriz de x filas y columanas y z=3 canales
imagenfatigaent4 <- imagenfatigaent4 [,,1] # Deja un solo canal
imagenfatigaent4t <- t(imagenfatigaent4)
imagenfatigaent4xey <- rbind(imagenfatigaent4,imagenfatigaent4t)
imagenfatigaent4xey <- t(imagenfatigaent4xey)
dim(imagenfatigaent4xey)## [1] 200 400imagenfatigaent5 <- read.bitmap("FatigaEnt5.jpg") # crea una matriz de x filas y columanas y z=3 canales
imagenfatigaent5 <- imagenfatigaent5 [,,1] # Deja un solo canal
imagenfatigaent5t <- t(imagenfatigaent5)
imagenfatigaent5xey <- rbind(imagenfatigaent5,imagenfatigaent5t)
imagenfatigaent5xey <- t(imagenfatigaent5xey)
dim(imagenfatigaent5xey)## [1] 200 400imagenfatigaent6 <- read.bitmap("FatigaEnt6.jpg") # crea una matriz de x filas y columanas y z=3 canales
imagenfatigaent6 <- imagenfatigaent6 [,,1] # Deja un solo canal
imagenfatigaent6t <- t(imagenfatigaent6)
imagenfatigaent6xey <- rbind(imagenfatigaent6,imagenfatigaent6t)
imagenfatigaent6xey <- t(imagenfatigaent6xey)
dim(imagenfatigaent6xey)## [1] 200 400imagenfatigaent7 <- read.bitmap("FatigaEnt7.jpg") # crea una matriz de x filas y columanas y z=3 canales
imagenfatigaent7 <- imagenfatigaent7 [,,1] # Deja un solo canal
imagenfatigaent7t <- t(imagenfatigaent7)
imagenfatigaent7xey <- rbind(imagenfatigaent7,imagenfatigaent7t)
imagenfatigaent7xey <- t(imagenfatigaent7xey)
dim(imagenfatigaent7xey)## [1] 200 400imagenfatigaens1 <- read.bitmap("FatigaEns1.jpg") # crea una matriz de x filas y columanas y z=3 canales
imagenfatigaens1 <- imagenfatigaens1 [,,1] # Deja un solo canal
imagenfatigaens1t <- t(imagenfatigaens1)
imagenfatigaens1xey <- rbind(imagenfatigaens1,imagenfatigaens1t)
imagenfatigaens1xey <- t(imagenfatigaens1xey)
dim(imagenfatigaens1xey)## [1] 200 400imagenfatigaens2 <- read.bitmap("FatigaEns2.jpg") # crea una matriz de x filas y columanas y z=3 canales
imagenfatigaens2 <- imagenfatigaens2 [,,1] # Deja un solo canal
imagenfatigaens2t <- t(imagenfatigaens2)
imagenfatigaens2xey <- rbind(imagenfatigaens2,imagenfatigaens2t)
imagenfatigaens2xey <- t(imagenfatigaens2xey)
dim(imagenfatigaens2xey)## [1] 200 400imagenfatigaens3 <- read.bitmap("FatigaEns3.jpg") # crea una matriz de x filas y columanas y z=3 canales
imagenfatigaens3 <- imagenfatigaens3 [,,1] # Deja un solo canal
imagenfatigaens3t <- t(imagenfatigaens3)
imagenfatigaens3xey <- rbind(imagenfatigaens3,imagenfatigaens3t)
imagenfatigaens3xey <- t(imagenfatigaens3xey)
dim(imagenfatigaens3xey)## [1] 200 400imagenfatigaxey <- cbind(imagenfatigaent1xey,imagenfatigaent2xey,imagenfatigaent3xey,imagenfatigaent4xey,imagenfatigaent5xey,imagenfatigaent6xey,imagenfatigaent7xey,imagenfatigaens1xey,imagenfatigaens2xey,imagenfatigaens3xey)
dim(imagenfatigaxey)## [1] 200 4000# Convertir en Data Frame fatiga
imagenfatigaxeydf <- as.data.frame (imagenfatigaxey)
attributes(imagenfatigaxeydf)## $names
## [1] "V1" "V2" "V3" "V4" "V5" "V6" "V7" "V8" "V9"
## [10] "V10" "V11" "V12" "V13" "V14" "V15" "V16" "V17" "V18"
## [19] "V19" "V20" "V21" "V22" "V23" "V24" "V25" "V26" "V27"
## [28] "V28" "V29" "V30" "V31" "V32" "V33" "V34" "V35" "V36"
## [37] "V37" "V38" "V39" "V40" "V41" "V42" "V43" "V44" "V45"
## [46] "V46" "V47" "V48" "V49" "V50" "V51" "V52" "V53" "V54"
## [55] "V55" "V56" "V57" "V58" "V59" "V60" "V61" "V62" "V63"
## [64] "V64" "V65" "V66" "V67" "V68" "V69" "V70" "V71" "V72"
## [73] "V73" "V74" "V75" "V76" "V77" "V78" "V79" "V80" "V81"
## [82] "V82" "V83" "V84" "V85" "V86" "V87" "V88" "V89" "V90"
## [91] "V91" "V92" "V93" "V94" "V95" "V96" "V97" "V98" "V99"
## [100] "V100" "V101" "V102" "V103" "V104" "V105" "V106" "V107" "V108"
## [109] "V109" "V110" "V111" "V112" "V113" "V114" "V115" "V116" "V117"
## [118] "V118" "V119" "V120" "V121" "V122" "V123" "V124" "V125" "V126"
## [127] "V127" "V128" "V129" "V130" "V131" "V132" "V133" "V134" "V135"
## [136] "V136" "V137" "V138" "V139" "V140" "V141" "V142" "V143" "V144"
## [145] "V145" "V146" "V147" "V148" "V149" "V150" "V151" "V152" "V153"
## [154] "V154" "V155" "V156" "V157" "V158" "V159" "V160" "V161" "V162"
## [163] "V163" "V164" "V165" "V166" "V167" "V168" "V169" "V170" "V171"
## [172] "V172" "V173" "V174" "V175" "V176" "V177" "V178" "V179" "V180"
## [181] "V181" "V182" "V183" "V184" "V185" "V186" "V187" "V188" "V189"
## [190] "V190" "V191" "V192" "V193" "V194" "V195" "V196" "V197" "V198"
## [199] "V199" "V200" "V201" "V202" "V203" "V204" "V205" "V206" "V207"
## [208] "V208" "V209" "V210" "V211" "V212" "V213" "V214" "V215" "V216"
## [217] "V217" "V218" "V219" "V220" "V221" "V222" "V223" "V224" "V225"
## [226] "V226" "V227" "V228" "V229" "V230" "V231" "V232" "V233" "V234"
## [235] "V235" "V236" "V237" "V238" "V239" "V240" "V241" "V242" "V243"
## [244] "V244" "V245" "V246" "V247" "V248" "V249" "V250" "V251" "V252"
## [253] "V253" "V254" "V255" "V256" "V257" "V258" "V259" "V260" "V261"
## [262] "V262" "V263" "V264" "V265" "V266" "V267" "V268" "V269" "V270"
## [271] "V271" "V272" "V273" "V274" "V275" "V276" "V277" "V278" "V279"
## [280] "V280" "V281" "V282" "V283" "V284" "V285" "V286" "V287" "V288"
## [289] "V289" "V290" "V291" "V292" "V293" "V294" "V295" "V296" "V297"
## [298] "V298" "V299" "V300" "V301" "V302" "V303" "V304" "V305" "V306"
## [307] "V307" "V308" "V309" "V310" "V311" "V312" "V313" "V314" "V315"
## [316] "V316" "V317" "V318" "V319" "V320" "V321" "V322" "V323" "V324"
## [325] "V325" "V326" "V327" "V328" "V329" "V330" "V331" "V332" "V333"
## [334] "V334" "V335" "V336" "V337" "V338" "V339" "V340" "V341" "V342"
## [343] "V343" "V344" "V345" "V346" "V347" "V348" "V349" "V350" "V351"
## [352] "V352" "V353" "V354" "V355" "V356" "V357" "V358" "V359" "V360"
## [361] "V361" "V362" "V363" "V364" "V365" "V366" "V367" "V368" "V369"
## [370] "V370" "V371" "V372" "V373" "V374" "V375" "V376" "V377" "V378"
## [379] "V379" "V380" "V381" "V382" "V383" "V384" "V385" "V386" "V387"
## [388] "V388" "V389" "V390" "V391" "V392" "V393" "V394" "V395" "V396"
## [397] "V397" "V398" "V399" "V400" "V401" "V402" "V403" "V404" "V405"
## [406] "V406" "V407" "V408" "V409" "V410" "V411" "V412" "V413" "V414"
## [415] "V415" "V416" "V417" "V418" "V419" "V420" "V421" "V422" "V423"
## [424] "V424" "V425" "V426" "V427" "V428" "V429" "V430" "V431" "V432"
## [433] "V433" "V434" "V435" "V436" "V437" "V438" "V439" "V440" "V441"
## [442] "V442" "V443" "V444" "V445" "V446" "V447" "V448" "V449" "V450"
## [451] "V451" "V452" "V453" "V454" "V455" "V456" "V457" "V458" "V459"
## [460] "V460" "V461" "V462" "V463" "V464" "V465" "V466" "V467" "V468"
## [469] "V469" "V470" "V471" "V472" "V473" "V474" "V475" "V476" "V477"
## [478] "V478" "V479" "V480" "V481" "V482" "V483" "V484" "V485" "V486"
## [487] "V487" "V488" "V489" "V490" "V491" "V492" "V493" "V494" "V495"
## [496] "V496" "V497" "V498" "V499" "V500" "V501" "V502" "V503" "V504"
## [505] "V505" "V506" "V507" "V508" "V509" "V510" "V511" "V512" "V513"
## [514] "V514" "V515" "V516" "V517" "V518" "V519" "V520" "V521" "V522"
## [523] "V523" "V524" "V525" "V526" "V527" "V528" "V529" "V530" "V531"
## [532] "V532" "V533" "V534" "V535" "V536" "V537" "V538" "V539" "V540"
## [541] "V541" "V542" "V543" "V544" "V545" "V546" "V547" "V548" "V549"
## [550] "V550" "V551" "V552" "V553" "V554" "V555" "V556" "V557" "V558"
## [559] "V559" "V560" "V561" "V562" "V563" "V564" "V565" "V566" "V567"
## [568] "V568" "V569" "V570" "V571" "V572" "V573" "V574" "V575" "V576"
## [577] "V577" "V578" "V579" "V580" "V581" "V582" "V583" "V584" "V585"
## [586] "V586" "V587" "V588" "V589" "V590" "V591" "V592" "V593" "V594"
## [595] "V595" "V596" "V597" "V598" "V599" "V600" "V601" "V602" "V603"
## [604] "V604" "V605" "V606" "V607" "V608" "V609" "V610" "V611" "V612"
## [613] "V613" "V614" "V615" "V616" "V617" "V618" "V619" "V620" "V621"
## [622] "V622" "V623" "V624" "V625" "V626" "V627" "V628" "V629" "V630"
## [631] "V631" "V632" "V633" "V634" "V635" "V636" "V637" "V638" "V639"
## [640] "V640" "V641" "V642" "V643" "V644" "V645" "V646" "V647" "V648"
## [649] "V649" "V650" "V651" "V652" "V653" "V654" "V655" "V656" "V657"
## [658] "V658" "V659" "V660" "V661" "V662" "V663" "V664" "V665" "V666"
## [667] "V667" "V668" "V669" "V670" "V671" "V672" "V673" "V674" "V675"
## [676] "V676" "V677" "V678" "V679" "V680" "V681" "V682" "V683" "V684"
## [685] "V685" "V686" "V687" "V688" "V689" "V690" "V691" "V692" "V693"
## [694] "V694" "V695" "V696" "V697" "V698" "V699" "V700" "V701" "V702"
## [703] "V703" "V704" "V705" "V706" "V707" "V708" "V709" "V710" "V711"
## [712] "V712" "V713" "V714" "V715" "V716" "V717" "V718" "V719" "V720"
## [721] "V721" "V722" "V723" "V724" "V725" "V726" "V727" "V728" "V729"
## [730] "V730" "V731" "V732" "V733" "V734" "V735" "V736" "V737" "V738"
## [739] "V739" "V740" "V741" "V742" "V743" "V744" "V745" "V746" "V747"
## [748] "V748" "V749" "V750" "V751" "V752" "V753" "V754" "V755" "V756"
## [757] "V757" "V758" "V759" "V760" "V761" "V762" "V763" "V764" "V765"
## [766] "V766" "V767" "V768" "V769" "V770" "V771" "V772" "V773" "V774"
## [775] "V775" "V776" "V777" "V778" "V779" "V780" "V781" "V782" "V783"
## [784] "V784" "V785" "V786" "V787" "V788" "V789" "V790" "V791" "V792"
## [793] "V793" "V794" "V795" "V796" "V797" "V798" "V799" "V800" "V801"
## [802] "V802" "V803" "V804" "V805" "V806" "V807" "V808" "V809" "V810"
## [811] "V811" "V812" "V813" "V814" "V815" "V816" "V817" "V818" "V819"
## [820] "V820" "V821" "V822" "V823" "V824" "V825" "V826" "V827" "V828"
## [829] "V829" "V830" "V831" "V832" "V833" "V834" "V835" "V836" "V837"
## [838] "V838" "V839" "V840" "V841" "V842" "V843" "V844" "V845" "V846"
## [847] "V847" "V848" "V849" "V850" "V851" "V852" "V853" "V854" "V855"
## [856] "V856" "V857" "V858" "V859" "V860" "V861" "V862" "V863" "V864"
## [865] "V865" "V866" "V867" "V868" "V869" "V870" "V871" "V872" "V873"
## [874] "V874" "V875" "V876" "V877" "V878" "V879" "V880" "V881" "V882"
## [883] "V883" "V884" "V885" "V886" "V887" "V888" "V889" "V890" "V891"
## [892] "V892" "V893" "V894" "V895" "V896" "V897" "V898" "V899" "V900"
## [901] "V901" "V902" "V903" "V904" "V905" "V906" "V907" "V908" "V909"
## [910] "V910" "V911" "V912" "V913" "V914" "V915" "V916" "V917" "V918"
## [919] "V919" "V920" "V921" "V922" "V923" "V924" "V925" "V926" "V927"
## [928] "V928" "V929" "V930" "V931" "V932" "V933" "V934" "V935" "V936"
## [937] "V937" "V938" "V939" "V940" "V941" "V942" "V943" "V944" "V945"
## [946] "V946" "V947" "V948" "V949" "V950" "V951" "V952" "V953" "V954"
## [955] "V955" "V956" "V957" "V958" "V959" "V960" "V961" "V962" "V963"
## [964] "V964" "V965" "V966" "V967" "V968" "V969" "V970" "V971" "V972"
## [973] "V973" "V974" "V975" "V976" "V977" "V978" "V979" "V980" "V981"
## [982] "V982" "V983" "V984" "V985" "V986" "V987" "V988" "V989" "V990"
## [991] "V991" "V992" "V993" "V994" "V995" "V996" "V997" "V998" "V999"
## [1000] "V1000" "V1001" "V1002" "V1003" "V1004" "V1005" "V1006" "V1007" "V1008"
## [1009] "V1009" "V1010" "V1011" "V1012" "V1013" "V1014" "V1015" "V1016" "V1017"
## [1018] "V1018" "V1019" "V1020" "V1021" "V1022" "V1023" "V1024" "V1025" "V1026"
## [1027] "V1027" "V1028" "V1029" "V1030" "V1031" "V1032" "V1033" "V1034" "V1035"
## [1036] "V1036" "V1037" "V1038" "V1039" "V1040" "V1041" "V1042" "V1043" "V1044"
## [1045] "V1045" "V1046" "V1047" "V1048" "V1049" "V1050" "V1051" "V1052" "V1053"
## [1054] "V1054" "V1055" "V1056" "V1057" "V1058" "V1059" "V1060" "V1061" "V1062"
## [1063] "V1063" "V1064" "V1065" "V1066" "V1067" "V1068" "V1069" "V1070" "V1071"
## [1072] "V1072" "V1073" "V1074" "V1075" "V1076" "V1077" "V1078" "V1079" "V1080"
## [1081] "V1081" "V1082" "V1083" "V1084" "V1085" "V1086" "V1087" "V1088" "V1089"
## [1090] "V1090" "V1091" "V1092" "V1093" "V1094" "V1095" "V1096" "V1097" "V1098"
## [1099] "V1099" "V1100" "V1101" "V1102" "V1103" "V1104" "V1105" "V1106" "V1107"
## [1108] "V1108" "V1109" "V1110" "V1111" "V1112" "V1113" "V1114" "V1115" "V1116"
## [1117] "V1117" "V1118" "V1119" "V1120" "V1121" "V1122" "V1123" "V1124" "V1125"
## [1126] "V1126" "V1127" "V1128" "V1129" "V1130" "V1131" "V1132" "V1133" "V1134"
## [1135] "V1135" "V1136" "V1137" "V1138" "V1139" "V1140" "V1141" "V1142" "V1143"
## [1144] "V1144" "V1145" "V1146" "V1147" "V1148" "V1149" "V1150" "V1151" "V1152"
## [1153] "V1153" "V1154" "V1155" "V1156" "V1157" "V1158" "V1159" "V1160" "V1161"
## [1162] "V1162" "V1163" "V1164" "V1165" "V1166" "V1167" "V1168" "V1169" "V1170"
## [1171] "V1171" "V1172" "V1173" "V1174" "V1175" "V1176" "V1177" "V1178" "V1179"
## [1180] "V1180" "V1181" "V1182" "V1183" "V1184" "V1185" "V1186" "V1187" "V1188"
## [1189] "V1189" "V1190" "V1191" "V1192" "V1193" "V1194" "V1195" "V1196" "V1197"
## [1198] "V1198" "V1199" "V1200" "V1201" "V1202" "V1203" "V1204" "V1205" "V1206"
## [1207] "V1207" "V1208" "V1209" "V1210" "V1211" "V1212" "V1213" "V1214" "V1215"
## [1216] "V1216" "V1217" "V1218" "V1219" "V1220" "V1221" "V1222" "V1223" "V1224"
## [1225] "V1225" "V1226" "V1227" "V1228" "V1229" "V1230" "V1231" "V1232" "V1233"
## [1234] "V1234" "V1235" "V1236" "V1237" "V1238" "V1239" "V1240" "V1241" "V1242"
## [1243] "V1243" "V1244" "V1245" "V1246" "V1247" "V1248" "V1249" "V1250" "V1251"
## [1252] "V1252" "V1253" "V1254" "V1255" "V1256" "V1257" "V1258" "V1259" "V1260"
## [1261] "V1261" "V1262" "V1263" "V1264" "V1265" "V1266" "V1267" "V1268" "V1269"
## [1270] "V1270" "V1271" "V1272" "V1273" "V1274" "V1275" "V1276" "V1277" "V1278"
## [1279] "V1279" "V1280" "V1281" "V1282" "V1283" "V1284" "V1285" "V1286" "V1287"
## [1288] "V1288" "V1289" "V1290" "V1291" "V1292" "V1293" "V1294" "V1295" "V1296"
## [1297] "V1297" "V1298" "V1299" "V1300" "V1301" "V1302" "V1303" "V1304" "V1305"
## [1306] "V1306" "V1307" "V1308" "V1309" "V1310" "V1311" "V1312" "V1313" "V1314"
## [1315] "V1315" "V1316" "V1317" "V1318" "V1319" "V1320" "V1321" "V1322" "V1323"
## [1324] "V1324" "V1325" "V1326" "V1327" "V1328" "V1329" "V1330" "V1331" "V1332"
## [1333] "V1333" "V1334" "V1335" "V1336" "V1337" "V1338" "V1339" "V1340" "V1341"
## [1342] "V1342" "V1343" "V1344" "V1345" "V1346" "V1347" "V1348" "V1349" "V1350"
## [1351] "V1351" "V1352" "V1353" "V1354" "V1355" "V1356" "V1357" "V1358" "V1359"
## [1360] "V1360" "V1361" "V1362" "V1363" "V1364" "V1365" "V1366" "V1367" "V1368"
## [1369] "V1369" "V1370" "V1371" "V1372" "V1373" "V1374" "V1375" "V1376" "V1377"
## [1378] "V1378" "V1379" "V1380" "V1381" "V1382" "V1383" "V1384" "V1385" "V1386"
## [1387] "V1387" "V1388" "V1389" "V1390" "V1391" "V1392" "V1393" "V1394" "V1395"
## [1396] "V1396" "V1397" "V1398" "V1399" "V1400" "V1401" "V1402" "V1403" "V1404"
## [1405] "V1405" "V1406" "V1407" "V1408" "V1409" "V1410" "V1411" "V1412" "V1413"
## [1414] "V1414" "V1415" "V1416" "V1417" "V1418" "V1419" "V1420" "V1421" "V1422"
## [1423] "V1423" "V1424" "V1425" "V1426" "V1427" "V1428" "V1429" "V1430" "V1431"
## [1432] "V1432" "V1433" "V1434" "V1435" "V1436" "V1437" "V1438" "V1439" "V1440"
## [1441] "V1441" "V1442" "V1443" "V1444" "V1445" "V1446" "V1447" "V1448" "V1449"
## [1450] "V1450" "V1451" "V1452" "V1453" "V1454" "V1455" "V1456" "V1457" "V1458"
## [1459] "V1459" "V1460" "V1461" "V1462" "V1463" "V1464" "V1465" "V1466" "V1467"
## [1468] "V1468" "V1469" "V1470" "V1471" "V1472" "V1473" "V1474" "V1475" "V1476"
## [1477] "V1477" "V1478" "V1479" "V1480" "V1481" "V1482" "V1483" "V1484" "V1485"
## [1486] "V1486" "V1487" "V1488" "V1489" "V1490" "V1491" "V1492" "V1493" "V1494"
## [1495] "V1495" "V1496" "V1497" "V1498" "V1499" "V1500" "V1501" "V1502" "V1503"
## [1504] "V1504" "V1505" "V1506" "V1507" "V1508" "V1509" "V1510" "V1511" "V1512"
## [1513] "V1513" "V1514" "V1515" "V1516" "V1517" "V1518" "V1519" "V1520" "V1521"
## [1522] "V1522" "V1523" "V1524" "V1525" "V1526" "V1527" "V1528" "V1529" "V1530"
## [1531] "V1531" "V1532" "V1533" "V1534" "V1535" "V1536" "V1537" "V1538" "V1539"
## [1540] "V1540" "V1541" "V1542" "V1543" "V1544" "V1545" "V1546" "V1547" "V1548"
## [1549] "V1549" "V1550" "V1551" "V1552" "V1553" "V1554" "V1555" "V1556" "V1557"
## [1558] "V1558" "V1559" "V1560" "V1561" "V1562" "V1563" "V1564" "V1565" "V1566"
## [1567] "V1567" "V1568" "V1569" "V1570" "V1571" "V1572" "V1573" "V1574" "V1575"
## [1576] "V1576" "V1577" "V1578" "V1579" "V1580" "V1581" "V1582" "V1583" "V1584"
## [1585] "V1585" "V1586" "V1587" "V1588" "V1589" "V1590" "V1591" "V1592" "V1593"
## [1594] "V1594" "V1595" "V1596" "V1597" "V1598" "V1599" "V1600" "V1601" "V1602"
## [1603] "V1603" "V1604" "V1605" "V1606" "V1607" "V1608" "V1609" "V1610" "V1611"
## [1612] "V1612" "V1613" "V1614" "V1615" "V1616" "V1617" "V1618" "V1619" "V1620"
## [1621] "V1621" "V1622" "V1623" "V1624" "V1625" "V1626" "V1627" "V1628" "V1629"
## [1630] "V1630" "V1631" "V1632" "V1633" "V1634" "V1635" "V1636" "V1637" "V1638"
## [1639] "V1639" "V1640" "V1641" "V1642" "V1643" "V1644" "V1645" "V1646" "V1647"
## [1648] "V1648" "V1649" "V1650" "V1651" "V1652" "V1653" "V1654" "V1655" "V1656"
## [1657] "V1657" "V1658" "V1659" "V1660" "V1661" "V1662" "V1663" "V1664" "V1665"
## [1666] "V1666" "V1667" "V1668" "V1669" "V1670" "V1671" "V1672" "V1673" "V1674"
## [1675] "V1675" "V1676" "V1677" "V1678" "V1679" "V1680" "V1681" "V1682" "V1683"
## [1684] "V1684" "V1685" "V1686" "V1687" "V1688" "V1689" "V1690" "V1691" "V1692"
## [1693] "V1693" "V1694" "V1695" "V1696" "V1697" "V1698" "V1699" "V1700" "V1701"
## [1702] "V1702" "V1703" "V1704" "V1705" "V1706" "V1707" "V1708" "V1709" "V1710"
## [1711] "V1711" "V1712" "V1713" "V1714" "V1715" "V1716" "V1717" "V1718" "V1719"
## [1720] "V1720" "V1721" "V1722" "V1723" "V1724" "V1725" "V1726" "V1727" "V1728"
## [1729] "V1729" "V1730" "V1731" "V1732" "V1733" "V1734" "V1735" "V1736" "V1737"
## [1738] "V1738" "V1739" "V1740" "V1741" "V1742" "V1743" "V1744" "V1745" "V1746"
## [1747] "V1747" "V1748" "V1749" "V1750" "V1751" "V1752" "V1753" "V1754" "V1755"
## [1756] "V1756" "V1757" "V1758" "V1759" "V1760" "V1761" "V1762" "V1763" "V1764"
## [1765] "V1765" "V1766" "V1767" "V1768" "V1769" "V1770" "V1771" "V1772" "V1773"
## [1774] "V1774" "V1775" "V1776" "V1777" "V1778" "V1779" "V1780" "V1781" "V1782"
## [1783] "V1783" "V1784" "V1785" "V1786" "V1787" "V1788" "V1789" "V1790" "V1791"
## [1792] "V1792" "V1793" "V1794" "V1795" "V1796" "V1797" "V1798" "V1799" "V1800"
## [1801] "V1801" "V1802" "V1803" "V1804" "V1805" "V1806" "V1807" "V1808" "V1809"
## [1810] "V1810" "V1811" "V1812" "V1813" "V1814" "V1815" "V1816" "V1817" "V1818"
## [1819] "V1819" "V1820" "V1821" "V1822" "V1823" "V1824" "V1825" "V1826" "V1827"
## [1828] "V1828" "V1829" "V1830" "V1831" "V1832" "V1833" "V1834" "V1835" "V1836"
## [1837] "V1837" "V1838" "V1839" "V1840" "V1841" "V1842" "V1843" "V1844" "V1845"
## [1846] "V1846" "V1847" "V1848" "V1849" "V1850" "V1851" "V1852" "V1853" "V1854"
## [1855] "V1855" "V1856" "V1857" "V1858" "V1859" "V1860" "V1861" "V1862" "V1863"
## [1864] "V1864" "V1865" "V1866" "V1867" "V1868" "V1869" "V1870" "V1871" "V1872"
## [1873] "V1873" "V1874" "V1875" "V1876" "V1877" "V1878" "V1879" "V1880" "V1881"
## [1882] "V1882" "V1883" "V1884" "V1885" "V1886" "V1887" "V1888" "V1889" "V1890"
## [1891] "V1891" "V1892" "V1893" "V1894" "V1895" "V1896" "V1897" "V1898" "V1899"
## [1900] "V1900" "V1901" "V1902" "V1903" "V1904" "V1905" "V1906" "V1907" "V1908"
## [1909] "V1909" "V1910" "V1911" "V1912" "V1913" "V1914" "V1915" "V1916" "V1917"
## [1918] "V1918" "V1919" "V1920" "V1921" "V1922" "V1923" "V1924" "V1925" "V1926"
## [1927] "V1927" "V1928" "V1929" "V1930" "V1931" "V1932" "V1933" "V1934" "V1935"
## [1936] "V1936" "V1937" "V1938" "V1939" "V1940" "V1941" "V1942" "V1943" "V1944"
## [1945] "V1945" "V1946" "V1947" "V1948" "V1949" "V1950" "V1951" "V1952" "V1953"
## [1954] "V1954" "V1955" "V1956" "V1957" "V1958" "V1959" "V1960" "V1961" "V1962"
## [1963] "V1963" "V1964" "V1965" "V1966" "V1967" "V1968" "V1969" "V1970" "V1971"
## [1972] "V1972" "V1973" "V1974" "V1975" "V1976" "V1977" "V1978" "V1979" "V1980"
## [1981] "V1981" "V1982" "V1983" "V1984" "V1985" "V1986" "V1987" "V1988" "V1989"
## [1990] "V1990" "V1991" "V1992" "V1993" "V1994" "V1995" "V1996" "V1997" "V1998"
## [1999] "V1999" "V2000" "V2001" "V2002" "V2003" "V2004" "V2005" "V2006" "V2007"
## [2008] "V2008" "V2009" "V2010" "V2011" "V2012" "V2013" "V2014" "V2015" "V2016"
## [2017] "V2017" "V2018" "V2019" "V2020" "V2021" "V2022" "V2023" "V2024" "V2025"
## [2026] "V2026" "V2027" "V2028" "V2029" "V2030" "V2031" "V2032" "V2033" "V2034"
## [2035] "V2035" "V2036" "V2037" "V2038" "V2039" "V2040" "V2041" "V2042" "V2043"
## [2044] "V2044" "V2045" "V2046" "V2047" "V2048" "V2049" "V2050" "V2051" "V2052"
## [2053] "V2053" "V2054" "V2055" "V2056" "V2057" "V2058" "V2059" "V2060" "V2061"
## [2062] "V2062" "V2063" "V2064" "V2065" "V2066" "V2067" "V2068" "V2069" "V2070"
## [2071] "V2071" "V2072" "V2073" "V2074" "V2075" "V2076" "V2077" "V2078" "V2079"
## [2080] "V2080" "V2081" "V2082" "V2083" "V2084" "V2085" "V2086" "V2087" "V2088"
## [2089] "V2089" "V2090" "V2091" "V2092" "V2093" "V2094" "V2095" "V2096" "V2097"
## [2098] "V2098" "V2099" "V2100" "V2101" "V2102" "V2103" "V2104" "V2105" "V2106"
## [2107] "V2107" "V2108" "V2109" "V2110" "V2111" "V2112" "V2113" "V2114" "V2115"
## [2116] "V2116" "V2117" "V2118" "V2119" "V2120" "V2121" "V2122" "V2123" "V2124"
## [2125] "V2125" "V2126" "V2127" "V2128" "V2129" "V2130" "V2131" "V2132" "V2133"
## [2134] "V2134" "V2135" "V2136" "V2137" "V2138" "V2139" "V2140" "V2141" "V2142"
## [2143] "V2143" "V2144" "V2145" "V2146" "V2147" "V2148" "V2149" "V2150" "V2151"
## [2152] "V2152" "V2153" "V2154" "V2155" "V2156" "V2157" "V2158" "V2159" "V2160"
## [2161] "V2161" "V2162" "V2163" "V2164" "V2165" "V2166" "V2167" "V2168" "V2169"
## [2170] "V2170" "V2171" "V2172" "V2173" "V2174" "V2175" "V2176" "V2177" "V2178"
## [2179] "V2179" "V2180" "V2181" "V2182" "V2183" "V2184" "V2185" "V2186" "V2187"
## [2188] "V2188" "V2189" "V2190" "V2191" "V2192" "V2193" "V2194" "V2195" "V2196"
## [2197] "V2197" "V2198" "V2199" "V2200" "V2201" "V2202" "V2203" "V2204" "V2205"
## [2206] "V2206" "V2207" "V2208" "V2209" "V2210" "V2211" "V2212" "V2213" "V2214"
## [2215] "V2215" "V2216" "V2217" "V2218" "V2219" "V2220" "V2221" "V2222" "V2223"
## [2224] "V2224" "V2225" "V2226" "V2227" "V2228" "V2229" "V2230" "V2231" "V2232"
## [2233] "V2233" "V2234" "V2235" "V2236" "V2237" "V2238" "V2239" "V2240" "V2241"
## [2242] "V2242" "V2243" "V2244" "V2245" "V2246" "V2247" "V2248" "V2249" "V2250"
## [2251] "V2251" "V2252" "V2253" "V2254" "V2255" "V2256" "V2257" "V2258" "V2259"
## [2260] "V2260" "V2261" "V2262" "V2263" "V2264" "V2265" "V2266" "V2267" "V2268"
## [2269] "V2269" "V2270" "V2271" "V2272" "V2273" "V2274" "V2275" "V2276" "V2277"
## [2278] "V2278" "V2279" "V2280" "V2281" "V2282" "V2283" "V2284" "V2285" "V2286"
## [2287] "V2287" "V2288" "V2289" "V2290" "V2291" "V2292" "V2293" "V2294" "V2295"
## [2296] "V2296" "V2297" "V2298" "V2299" "V2300" "V2301" "V2302" "V2303" "V2304"
## [2305] "V2305" "V2306" "V2307" "V2308" "V2309" "V2310" "V2311" "V2312" "V2313"
## [2314] "V2314" "V2315" "V2316" "V2317" "V2318" "V2319" "V2320" "V2321" "V2322"
## [2323] "V2323" "V2324" "V2325" "V2326" "V2327" "V2328" "V2329" "V2330" "V2331"
## [2332] "V2332" "V2333" "V2334" "V2335" "V2336" "V2337" "V2338" "V2339" "V2340"
## [2341] "V2341" "V2342" "V2343" "V2344" "V2345" "V2346" "V2347" "V2348" "V2349"
## [2350] "V2350" "V2351" "V2352" "V2353" "V2354" "V2355" "V2356" "V2357" "V2358"
## [2359] "V2359" "V2360" "V2361" "V2362" "V2363" "V2364" "V2365" "V2366" "V2367"
## [2368] "V2368" "V2369" "V2370" "V2371" "V2372" "V2373" "V2374" "V2375" "V2376"
## [2377] "V2377" "V2378" "V2379" "V2380" "V2381" "V2382" "V2383" "V2384" "V2385"
## [2386] "V2386" "V2387" "V2388" "V2389" "V2390" "V2391" "V2392" "V2393" "V2394"
## [2395] "V2395" "V2396" "V2397" "V2398" "V2399" "V2400" "V2401" "V2402" "V2403"
## [2404] "V2404" "V2405" "V2406" "V2407" "V2408" "V2409" "V2410" "V2411" "V2412"
## [2413] "V2413" "V2414" "V2415" "V2416" "V2417" "V2418" "V2419" "V2420" "V2421"
## [2422] "V2422" "V2423" "V2424" "V2425" "V2426" "V2427" "V2428" "V2429" "V2430"
## [2431] "V2431" "V2432" "V2433" "V2434" "V2435" "V2436" "V2437" "V2438" "V2439"
## [2440] "V2440" "V2441" "V2442" "V2443" "V2444" "V2445" "V2446" "V2447" "V2448"
## [2449] "V2449" "V2450" "V2451" "V2452" "V2453" "V2454" "V2455" "V2456" "V2457"
## [2458] "V2458" "V2459" "V2460" "V2461" "V2462" "V2463" "V2464" "V2465" "V2466"
## [2467] "V2467" "V2468" "V2469" "V2470" "V2471" "V2472" "V2473" "V2474" "V2475"
## [2476] "V2476" "V2477" "V2478" "V2479" "V2480" "V2481" "V2482" "V2483" "V2484"
## [2485] "V2485" "V2486" "V2487" "V2488" "V2489" "V2490" "V2491" "V2492" "V2493"
## [2494] "V2494" "V2495" "V2496" "V2497" "V2498" "V2499" "V2500" "V2501" "V2502"
## [2503] "V2503" "V2504" "V2505" "V2506" "V2507" "V2508" "V2509" "V2510" "V2511"
## [2512] "V2512" "V2513" "V2514" "V2515" "V2516" "V2517" "V2518" "V2519" "V2520"
## [2521] "V2521" "V2522" "V2523" "V2524" "V2525" "V2526" "V2527" "V2528" "V2529"
## [2530] "V2530" "V2531" "V2532" "V2533" "V2534" "V2535" "V2536" "V2537" "V2538"
## [2539] "V2539" "V2540" "V2541" "V2542" "V2543" "V2544" "V2545" "V2546" "V2547"
## [2548] "V2548" "V2549" "V2550" "V2551" "V2552" "V2553" "V2554" "V2555" "V2556"
## [2557] "V2557" "V2558" "V2559" "V2560" "V2561" "V2562" "V2563" "V2564" "V2565"
## [2566] "V2566" "V2567" "V2568" "V2569" "V2570" "V2571" "V2572" "V2573" "V2574"
## [2575] "V2575" "V2576" "V2577" "V2578" "V2579" "V2580" "V2581" "V2582" "V2583"
## [2584] "V2584" "V2585" "V2586" "V2587" "V2588" "V2589" "V2590" "V2591" "V2592"
## [2593] "V2593" "V2594" "V2595" "V2596" "V2597" "V2598" "V2599" "V2600" "V2601"
## [2602] "V2602" "V2603" "V2604" "V2605" "V2606" "V2607" "V2608" "V2609" "V2610"
## [2611] "V2611" "V2612" "V2613" "V2614" "V2615" "V2616" "V2617" "V2618" "V2619"
## [2620] "V2620" "V2621" "V2622" "V2623" "V2624" "V2625" "V2626" "V2627" "V2628"
## [2629] "V2629" "V2630" "V2631" "V2632" "V2633" "V2634" "V2635" "V2636" "V2637"
## [2638] "V2638" "V2639" "V2640" "V2641" "V2642" "V2643" "V2644" "V2645" "V2646"
## [2647] "V2647" "V2648" "V2649" "V2650" "V2651" "V2652" "V2653" "V2654" "V2655"
## [2656] "V2656" "V2657" "V2658" "V2659" "V2660" "V2661" "V2662" "V2663" "V2664"
## [2665] "V2665" "V2666" "V2667" "V2668" "V2669" "V2670" "V2671" "V2672" "V2673"
## [2674] "V2674" "V2675" "V2676" "V2677" "V2678" "V2679" "V2680" "V2681" "V2682"
## [2683] "V2683" "V2684" "V2685" "V2686" "V2687" "V2688" "V2689" "V2690" "V2691"
## [2692] "V2692" "V2693" "V2694" "V2695" "V2696" "V2697" "V2698" "V2699" "V2700"
## [2701] "V2701" "V2702" "V2703" "V2704" "V2705" "V2706" "V2707" "V2708" "V2709"
## [2710] "V2710" "V2711" "V2712" "V2713" "V2714" "V2715" "V2716" "V2717" "V2718"
## [2719] "V2719" "V2720" "V2721" "V2722" "V2723" "V2724" "V2725" "V2726" "V2727"
## [2728] "V2728" "V2729" "V2730" "V2731" "V2732" "V2733" "V2734" "V2735" "V2736"
## [2737] "V2737" "V2738" "V2739" "V2740" "V2741" "V2742" "V2743" "V2744" "V2745"
## [2746] "V2746" "V2747" "V2748" "V2749" "V2750" "V2751" "V2752" "V2753" "V2754"
## [2755] "V2755" "V2756" "V2757" "V2758" "V2759" "V2760" "V2761" "V2762" "V2763"
## [2764] "V2764" "V2765" "V2766" "V2767" "V2768" "V2769" "V2770" "V2771" "V2772"
## [2773] "V2773" "V2774" "V2775" "V2776" "V2777" "V2778" "V2779" "V2780" "V2781"
## [2782] "V2782" "V2783" "V2784" "V2785" "V2786" "V2787" "V2788" "V2789" "V2790"
## [2791] "V2791" "V2792" "V2793" "V2794" "V2795" "V2796" "V2797" "V2798" "V2799"
## [2800] "V2800" "V2801" "V2802" "V2803" "V2804" "V2805" "V2806" "V2807" "V2808"
## [2809] "V2809" "V2810" "V2811" "V2812" "V2813" "V2814" "V2815" "V2816" "V2817"
## [2818] "V2818" "V2819" "V2820" "V2821" "V2822" "V2823" "V2824" "V2825" "V2826"
## [2827] "V2827" "V2828" "V2829" "V2830" "V2831" "V2832" "V2833" "V2834" "V2835"
## [2836] "V2836" "V2837" "V2838" "V2839" "V2840" "V2841" "V2842" "V2843" "V2844"
## [2845] "V2845" "V2846" "V2847" "V2848" "V2849" "V2850" "V2851" "V2852" "V2853"
## [2854] "V2854" "V2855" "V2856" "V2857" "V2858" "V2859" "V2860" "V2861" "V2862"
## [2863] "V2863" "V2864" "V2865" "V2866" "V2867" "V2868" "V2869" "V2870" "V2871"
## [2872] "V2872" "V2873" "V2874" "V2875" "V2876" "V2877" "V2878" "V2879" "V2880"
## [2881] "V2881" "V2882" "V2883" "V2884" "V2885" "V2886" "V2887" "V2888" "V2889"
## [2890] "V2890" "V2891" "V2892" "V2893" "V2894" "V2895" "V2896" "V2897" "V2898"
## [2899] "V2899" "V2900" "V2901" "V2902" "V2903" "V2904" "V2905" "V2906" "V2907"
## [2908] "V2908" "V2909" "V2910" "V2911" "V2912" "V2913" "V2914" "V2915" "V2916"
## [2917] "V2917" "V2918" "V2919" "V2920" "V2921" "V2922" "V2923" "V2924" "V2925"
## [2926] "V2926" "V2927" "V2928" "V2929" "V2930" "V2931" "V2932" "V2933" "V2934"
## [2935] "V2935" "V2936" "V2937" "V2938" "V2939" "V2940" "V2941" "V2942" "V2943"
## [2944] "V2944" "V2945" "V2946" "V2947" "V2948" "V2949" "V2950" "V2951" "V2952"
## [2953] "V2953" "V2954" "V2955" "V2956" "V2957" "V2958" "V2959" "V2960" "V2961"
## [2962] "V2962" "V2963" "V2964" "V2965" "V2966" "V2967" "V2968" "V2969" "V2970"
## [2971] "V2971" "V2972" "V2973" "V2974" "V2975" "V2976" "V2977" "V2978" "V2979"
## [2980] "V2980" "V2981" "V2982" "V2983" "V2984" "V2985" "V2986" "V2987" "V2988"
## [2989] "V2989" "V2990" "V2991" "V2992" "V2993" "V2994" "V2995" "V2996" "V2997"
## [2998] "V2998" "V2999" "V3000" "V3001" "V3002" "V3003" "V3004" "V3005" "V3006"
## [3007] "V3007" "V3008" "V3009" "V3010" "V3011" "V3012" "V3013" "V3014" "V3015"
## [3016] "V3016" "V3017" "V3018" "V3019" "V3020" "V3021" "V3022" "V3023" "V3024"
## [3025] "V3025" "V3026" "V3027" "V3028" "V3029" "V3030" "V3031" "V3032" "V3033"
## [3034] "V3034" "V3035" "V3036" "V3037" "V3038" "V3039" "V3040" "V3041" "V3042"
## [3043] "V3043" "V3044" "V3045" "V3046" "V3047" "V3048" "V3049" "V3050" "V3051"
## [3052] "V3052" "V3053" "V3054" "V3055" "V3056" "V3057" "V3058" "V3059" "V3060"
## [3061] "V3061" "V3062" "V3063" "V3064" "V3065" "V3066" "V3067" "V3068" "V3069"
## [3070] "V3070" "V3071" "V3072" "V3073" "V3074" "V3075" "V3076" "V3077" "V3078"
## [3079] "V3079" "V3080" "V3081" "V3082" "V3083" "V3084" "V3085" "V3086" "V3087"
## [3088] "V3088" "V3089" "V3090" "V3091" "V3092" "V3093" "V3094" "V3095" "V3096"
## [3097] "V3097" "V3098" "V3099" "V3100" "V3101" "V3102" "V3103" "V3104" "V3105"
## [3106] "V3106" "V3107" "V3108" "V3109" "V3110" "V3111" "V3112" "V3113" "V3114"
## [3115] "V3115" "V3116" "V3117" "V3118" "V3119" "V3120" "V3121" "V3122" "V3123"
## [3124] "V3124" "V3125" "V3126" "V3127" "V3128" "V3129" "V3130" "V3131" "V3132"
## [3133] "V3133" "V3134" "V3135" "V3136" "V3137" "V3138" "V3139" "V3140" "V3141"
## [3142] "V3142" "V3143" "V3144" "V3145" "V3146" "V3147" "V3148" "V3149" "V3150"
## [3151] "V3151" "V3152" "V3153" "V3154" "V3155" "V3156" "V3157" "V3158" "V3159"
## [3160] "V3160" "V3161" "V3162" "V3163" "V3164" "V3165" "V3166" "V3167" "V3168"
## [3169] "V3169" "V3170" "V3171" "V3172" "V3173" "V3174" "V3175" "V3176" "V3177"
## [3178] "V3178" "V3179" "V3180" "V3181" "V3182" "V3183" "V3184" "V3185" "V3186"
## [3187] "V3187" "V3188" "V3189" "V3190" "V3191" "V3192" "V3193" "V3194" "V3195"
## [3196] "V3196" "V3197" "V3198" "V3199" "V3200" "V3201" "V3202" "V3203" "V3204"
## [3205] "V3205" "V3206" "V3207" "V3208" "V3209" "V3210" "V3211" "V3212" "V3213"
## [3214] "V3214" "V3215" "V3216" "V3217" "V3218" "V3219" "V3220" "V3221" "V3222"
## [3223] "V3223" "V3224" "V3225" "V3226" "V3227" "V3228" "V3229" "V3230" "V3231"
## [3232] "V3232" "V3233" "V3234" "V3235" "V3236" "V3237" "V3238" "V3239" "V3240"
## [3241] "V3241" "V3242" "V3243" "V3244" "V3245" "V3246" "V3247" "V3248" "V3249"
## [3250] "V3250" "V3251" "V3252" "V3253" "V3254" "V3255" "V3256" "V3257" "V3258"
## [3259] "V3259" "V3260" "V3261" "V3262" "V3263" "V3264" "V3265" "V3266" "V3267"
## [3268] "V3268" "V3269" "V3270" "V3271" "V3272" "V3273" "V3274" "V3275" "V3276"
## [3277] "V3277" "V3278" "V3279" "V3280" "V3281" "V3282" "V3283" "V3284" "V3285"
## [3286] "V3286" "V3287" "V3288" "V3289" "V3290" "V3291" "V3292" "V3293" "V3294"
## [3295] "V3295" "V3296" "V3297" "V3298" "V3299" "V3300" "V3301" "V3302" "V3303"
## [3304] "V3304" "V3305" "V3306" "V3307" "V3308" "V3309" "V3310" "V3311" "V3312"
## [3313] "V3313" "V3314" "V3315" "V3316" "V3317" "V3318" "V3319" "V3320" "V3321"
## [3322] "V3322" "V3323" "V3324" "V3325" "V3326" "V3327" "V3328" "V3329" "V3330"
## [3331] "V3331" "V3332" "V3333" "V3334" "V3335" "V3336" "V3337" "V3338" "V3339"
## [3340] "V3340" "V3341" "V3342" "V3343" "V3344" "V3345" "V3346" "V3347" "V3348"
## [3349] "V3349" "V3350" "V3351" "V3352" "V3353" "V3354" "V3355" "V3356" "V3357"
## [3358] "V3358" "V3359" "V3360" "V3361" "V3362" "V3363" "V3364" "V3365" "V3366"
## [3367] "V3367" "V3368" "V3369" "V3370" "V3371" "V3372" "V3373" "V3374" "V3375"
## [3376] "V3376" "V3377" "V3378" "V3379" "V3380" "V3381" "V3382" "V3383" "V3384"
## [3385] "V3385" "V3386" "V3387" "V3388" "V3389" "V3390" "V3391" "V3392" "V3393"
## [3394] "V3394" "V3395" "V3396" "V3397" "V3398" "V3399" "V3400" "V3401" "V3402"
## [3403] "V3403" "V3404" "V3405" "V3406" "V3407" "V3408" "V3409" "V3410" "V3411"
## [3412] "V3412" "V3413" "V3414" "V3415" "V3416" "V3417" "V3418" "V3419" "V3420"
## [3421] "V3421" "V3422" "V3423" "V3424" "V3425" "V3426" "V3427" "V3428" "V3429"
## [3430] "V3430" "V3431" "V3432" "V3433" "V3434" "V3435" "V3436" "V3437" "V3438"
## [3439] "V3439" "V3440" "V3441" "V3442" "V3443" "V3444" "V3445" "V3446" "V3447"
## [3448] "V3448" "V3449" "V3450" "V3451" "V3452" "V3453" "V3454" "V3455" "V3456"
## [3457] "V3457" "V3458" "V3459" "V3460" "V3461" "V3462" "V3463" "V3464" "V3465"
## [3466] "V3466" "V3467" "V3468" "V3469" "V3470" "V3471" "V3472" "V3473" "V3474"
## [3475] "V3475" "V3476" "V3477" "V3478" "V3479" "V3480" "V3481" "V3482" "V3483"
## [3484] "V3484" "V3485" "V3486" "V3487" "V3488" "V3489" "V3490" "V3491" "V3492"
## [3493] "V3493" "V3494" "V3495" "V3496" "V3497" "V3498" "V3499" "V3500" "V3501"
## [3502] "V3502" "V3503" "V3504" "V3505" "V3506" "V3507" "V3508" "V3509" "V3510"
## [3511] "V3511" "V3512" "V3513" "V3514" "V3515" "V3516" "V3517" "V3518" "V3519"
## [3520] "V3520" "V3521" "V3522" "V3523" "V3524" "V3525" "V3526" "V3527" "V3528"
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##
## $class
## [1] "data.frame"
##
## $row.names
## [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
## [19] 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
## [37] 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54
## [55] 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72
## [73] 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90
## [91] 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108
## [109] 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126
## [127] 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144
## [145] 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162
## [163] 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180
## [181] 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198
## [199] 199 200# las filas son el número de puntos de evaluación de la función y las columnas el número de curvas
# Suavizamiento spline
# Creación de la base de funciones
npuntos <- nrow(imagenfatigaxeydf)
base_bspline <- create.bspline.basis(c(1, npuntos), 150)
plot(base_bspline)
summary(base_bspline)##
## Basis object:
##
## Type: bspline
##
## Range: 1 to 200
##
## Number of basis functions: 150# Selección de lambda
gcv <- NULL
lambda_list <- seq(-2, 4, length.out = 30)
# estos son las potencias de 10 de variación del lambda
# inicia con valores muy cercanos a cero 10^-2 hasta 10^4
matrix_data <- as.matrix(imagenfatigaxeydf)
for (lambda in lambda_list) {
lambda <- 10**lambda
param_lambda <- fdPar(base_bspline,
2,
lambda)
fd_smoothfatiga <- smooth.basis(argvals = seq(1,
nrow(matrix_data)),
y = matrix_data,
fdParobj = param_lambda)
gcv <- c(gcv, sum(fd_smoothfatiga$gcv))
}
# Se esta tomando como criterio total la suma de las VC de todas las curvas
plotgcv <-
data.frame(log_lambda = lambda_list,
gcv = gcv) %>% ggplot(aes(x = log_lambda, y = gcv)) +
geom_line(color = "purple", linetype = "dashed") +
theme_light() +
scale_x_continuous(limits = c(0, 4))
plotly::ggplotly(plotgcv)selected_lamdba <- 10**lambda_list[which.min(gcv)]
print(selected_lamdba)## [1] 0.04175319print(log(selected_lamdba, 10))## [1] -1.37931# entrega el valor de lambda donde se minimiza la suma de VC y log de lambda
# Suavizamiento con el lambda elegido
param_lambda <- fdPar(base_bspline,
2,
lambda = selected_lamdba)
fd_smoothfatiga <- smooth.basis(argvals = seq(1,
nrow(matrix_data)),
y = matrix_data,
fdParobj = param_lambda)
plot(fd_smoothfatiga, xlab= "Pixel", ylab = "Intensidad Totas Las Imagenes")
## [1] "done"# una curva por cada foto
# Comparación de curvas originales y suavizadas
fd_fittedfatiga <- fitted(fd_smoothfatiga)
plot(imagenfatigaxey[,1],type = "o",xlab="Pixel",ylab="Intensidad Ent1")
lines(fd_fittedfatiga[,1],col="2")
plot(imagenfatigaxey[,401],type = "o",xlab="Pixel",ylab="Intensidad Ent2")
lines(fd_fittedfatiga[,401],col="2")
plot(imagenfatigaxey[,801],type = "o",xlab="Pixel",ylab="Intensidad Ent3")
lines(fd_fittedfatiga[,801],col="2")
plot(imagenfatigaxey[,1201],type = "o",xlab="Pixel",ylab="Intensidad Ent4")
lines(fd_fittedfatiga[,1201],col="2")
plot(imagenfatigaxey[,1601],type = "o",xlab="Pixel",ylab="Intensidad Ent5")
lines(fd_fittedfatiga[,1601],col="2")
plot(imagenfatigaxey[,2001],type = "o",xlab="Pixel",ylab="Intensidad Ent6")
lines(fd_fittedfatiga[,2001],col="2")
plot(imagenfatigaxey[,2401],type = "o",xlab="Pixel",ylab="Intensidad Ent7")
lines(fd_fittedfatiga[,2401],col="2")
plot(imagenfatigaxey[,2801],type = "o",xlab="Pixel",ylab="Intensidad Ens1")
lines(fd_fittedfatiga[,2801],col="2")
plot(imagenfatigaxey[,3201],type = "o",xlab="Pixel",ylab="Intensidad Ens2")
lines(fd_fittedfatiga[,3201],col="2")
plot(imagenfatigaxey[,3601],type = "o",xlab="Pixel",ylab="Intensidad Ens3")
lines(fd_fittedfatiga[,3601],col="2")
3.1 Función de varianza imagen fatiga
Para ello se usa la función var.fd. En este caso se divide el recorrido en 200 puntos (igual que los pixeles).
Se calcula el operador de los datos de entrenamiento como conjunto y el de cada imagen de ensayo por separado.
var_fdfatigaEnt <- var.fd(fd_smoothfatiga$fd[1:2800])
var_fdfatigaEns1 <- var.fd(fd_smoothfatiga$fd[2801:3200])
var_fdfatigaEns2 <- var.fd(fd_smoothfatiga$fd[3201:3600])
var_fdfatigaEns3 <- var.fd(fd_smoothfatiga$fd[3601:4000])
# Calcula la varianza del objeto funcional de cada imagen
# La salida es un objeto bivariado funcional
# Necesita dos bases una para cada eje
eva <- seq(1, npuntos, length = 200)
matriz_var_fatigaEnt <- eval.bifd(eva, eva, var_fdfatigaEnt)
matriz_var_fatigaEns1 <- eval.bifd(eva, eva, var_fdfatigaEns1)
matriz_var_fatigaEns2 <- eval.bifd(eva, eva, var_fdfatigaEns2)
matriz_var_fatigaEns3 <- eval.bifd(eva, eva, var_fdfatigaEns3)4. Distancias imagenes ductiles de ensayo a cada grupo
Adjudica dos imagenes a fatiga y una a dúctil. 33% de Acierto.
distcov(matriz_var_ductilEnt, matriz_var_ductilEns1, method="Procrustes")## [1] 0.7707558distcov(matriz_var_fragilEnt, matriz_var_ductilEns1, method="Procrustes")## [1] 0.945329distcov(matriz_var_fatigaEnt, matriz_var_ductilEns1, method="Procrustes")## [1] 0.9858482distcov(matriz_var_ductilEnt, matriz_var_ductilEns2, method="Procrustes")## [1] 0.6602778distcov(matriz_var_fragilEnt, matriz_var_ductilEns2, method="Procrustes")## [1] 0.9477591distcov(matriz_var_fatigaEnt, matriz_var_ductilEns2, method="Procrustes")## [1] 0.6240316distcov(matriz_var_ductilEnt, matriz_var_ductilEns3, method="Procrustes")## [1] 0.628378distcov(matriz_var_fragilEnt, matriz_var_ductilEns3, method="Procrustes")## [1] 0.8546447distcov(matriz_var_fatigaEnt, matriz_var_ductilEns3, method="Procrustes")## [1] 0.60855885. Distancias imagenes fragiles de ensayo a cada grupo
Adjudica las imagenes a frágil. 100% de Aciertos.
distcov(matriz_var_ductilEnt, matriz_var_fragilEns1, method="Procrustes")## [1] 0.9602823distcov(matriz_var_fragilEnt, matriz_var_fragilEns1, method="Procrustes")## [1] 0.8295096distcov(matriz_var_fatigaEnt, matriz_var_fragilEns1, method="Procrustes")## [1] 1.151088distcov(matriz_var_ductilEnt, matriz_var_fragilEns2, method="Procrustes")## [1] 0.9140348distcov(matriz_var_fragilEnt, matriz_var_fragilEns2, method="Procrustes")## [1] 0.8211044distcov(matriz_var_fatigaEnt, matriz_var_fragilEns2, method="Procrustes")## [1] 1.087279distcov(matriz_var_ductilEnt, matriz_var_fragilEns3, method="Procrustes")## [1] 0.8680529distcov(matriz_var_fragilEnt, matriz_var_fragilEns3, method="Procrustes")## [1] 0.7985071distcov(matriz_var_fatigaEnt, matriz_var_fragilEns3, method="Procrustes")## [1] 0.99661436. Distancias imagenes fatiga de ensayo a cada grupo
Adjudica tres imagenes a fatiga. 100% de Aciertos.
distcov(matriz_var_ductilEnt, matriz_var_fatigaEns1, method="Procrustes")## [1] 0.8061949distcov(matriz_var_fragilEnt, matriz_var_fatigaEns1, method="Procrustes")## [1] 1.218664distcov(matriz_var_fatigaEnt, matriz_var_fatigaEns1, method="Procrustes")## [1] 0.5863577distcov(matriz_var_ductilEnt, matriz_var_fatigaEns2, method="Procrustes")## [1] 0.7081192distcov(matriz_var_fragilEnt, matriz_var_fatigaEns2, method="Procrustes")## [1] 1.015466distcov(matriz_var_fatigaEnt, matriz_var_fatigaEns2, method="Procrustes")## [1] 0.5666836distcov(matriz_var_ductilEnt, matriz_var_fatigaEns3, method="Procrustes")## [1] 0.8282263distcov(matriz_var_fragilEnt, matriz_var_fatigaEns3, method="Procrustes")## [1] 1.181704distcov(matriz_var_fatigaEnt, matriz_var_fatigaEns3, method="Procrustes")## [1] 0.5156258En conjunto se tiene una fracción de acierto de 0.7777. La falta de acierto se dio en dos imagenes dúctiles que se clasificaron como fatiga, sin embargo en la segunda opción de clasificación se adjudican a dúctil, Lo anterior se debe al importante traslape entre fatiga y dúctil de acuerdo a las gráficas de score en los componentes principales.